All of Norse mythology is very tentative; it just looks more certain because popular accounts treat the written sources uncritically. When it comes to written sources, those are mainly the Eddas. The elder Edda is a collection of older Skaldic poetry, the younger is written by the Icelander Snorri Sturluson in the 13th century as a guide to writing Skaldic poetry. The point of these works was not to accurately depict the pre-Christian religion but to continue the tradition of composing Skaldic poetry and telling these stories loosely based on historical figures their ancestors had mistakenly believed were gods. (in the view of Snorri and others of his time)

This fact, along with the fact that there was no single Norse religion in the first place, it was very hetereogenous with both time and place, is illustrated very well by the case of Ullr. This is a god who is barely mentioned in the Eddas, and the most substantial text is the short description Snorri wrote in Gylfaginning: "There is one named Ullr, Sif's son, Thor's stepson. He's a bow-man and such a good skier that noone can compete with him. He is also beatiful looking and of a warrior's disposition. It is good to call upon him in single combat."

There are also some older kennings (bynames) in the Skaldic poetry that associate him with skis and bows. That can't be taken as a second source though because these are not independent; it's possible (or even likely) Snorri himself inferred the fact that he was good at skiing and archery from the kennings. Notably, it doesn't explicitly say he's the god of archery, or god of skiing (i.e. using the genitive). So those may just be attributes (and later-day ones) rather than anything to do with his religious function. The roles of the gods in the stories are not necessarily related to their religious functions in previous days, where they had one. (Loki for instance is big in the stories but may not have had any religious role as far as can be seen from material sources) Even Thor, who was most definitely venerated, is described as being venerated as a weather god responsible for good harvests by Adam of Bremen in the 11th century, while he was still being worshiped. That's a rather different image from the Eddas. (not that the Edda image is consistent. Thor in Lokasenna is quite different in character from Thor in Alvíssmál) Another contradiction with Ullr as a skiing and hunting/archery god is that those same things are also attributed to Skaði later in Gylfaginning.

While there is little attestation of any veneration of popular mythological story gods like Heimdallr and Loki, there is evidence of worship of gods who have no mention in the Eddas (Like Þalfa, possibly Þjalfa), and for Ullr there is widespread evidence from place names that Ullr was widely venerated. There is namely a lot of place names dedicated to Ullr but they (like a lot of other such place names) are clustered to certain locales - Ullr seeming to have enjoyed most popularity in Uppland, Södermanland and parts of Östergötland in Sweden, and Vestfold, Østfold and Akershus in Norway. (Note: there's the famous Ullevi stadium in Gothenburg but that name is not older than the first stadium there, and based on an interpretation of Ull as being a god of games )

Stunningly, there are more places named "Ullevi" (and variants), indicating a ví (sacred site) dedicated to Ullr in Sweden than to any other god. 23 of them for Ullr vs 6 for Odin and only a single for Thor. (Thor's theophoric place-names are instead dominated by 12 places named "Torslunda", indicating a sacred grove)

In those terms, one would argue that Ullr ought to be a main figure in the pantheon, not a marginal ski-god. Why does he feature so little in the literature? There are several possible explanations. One is the geography; if Ullr was primarily a Swedish deity, it would be reason the Icelanders may not have had much knowledge or interest in him. However, on the other hand we have Adam of Bremen not mentioning anything about Ullr even though he was writing about paganism in Uppsala/Uppland, which is full of vi sites to Ullr. And there _are _ after all some Ullr sites in Norway which was much closer to Iceland culturally and geographically. There are three 'Ullinshof' sites, where a hof was a sacred site and perhaps the West Norse name for, or equivalent of, a vi (being that the term 'vi' doesn't seem to have been used there).

Only one Ullevi site (or indeed vi site for any god) has been excavated though, Lilla Ullevi in Upplands-Bro. The site was not known (besides the name) prior to excavation and the results were quite suprising. It'd been used since the Bronze Age but its ritual seems to have culminated during the Vendel Period (550-790) and ended with the site being intentionally covered over in the late 8th century. It is of course difficult to generalize from a single example but it raises the question of whether the cult of Ullr went out of fashion for one reason or another with the cultural changes that saw the end of the Vendel Period and beginning of the Viking Age. Ullr may have been little-known to medieval Icelanders because he'd not been venerated for 400 years.

So as for your question we know very little about Ullr. The written sources say very little and the fact that they do so may say more about how little they actually say about the cult that'd existed centuries prior. We don't know how Ullr or any other god was invoked or really any of the finer details of religious ritual. We know sacrifices were performed and we know for the layout of the Lilla Ullevi site, where a paved area was enclosed by fencing, there were posts with amulet-rings (which archaeology suggests were very important, and not just for Ullr, but the written sources say nothing about them). There was probably a big slab of a table on which sacrifices were made. There's no way of knowing what they said or did while doing it though. Christian Scandinavians (including Snorri) do not seem to have had an interest in documenting how to perform pagan rituals, and by the 13th century it's not that likely they could've if they'd wanted to.

Norse mythology doesn't have 'patron saints'. There's no Scandinavian tradition of wearing Ullr medallions while skiing (former or present-day). Whether invented by your parents or not that surely a modern invention and not one I recognize from here in Scandinavia. We don't know of any symbols or talismans that represent Ullr, or any representations of Ullr. The hunting motif on the Böksta stone has been speculated to have Ullr on it, but that's literally just because the figure has skis and a bow. Given the dating of c1020-1050 it's a bit of a coin toss whether it was raised by Christians or pagans in the first place (and being made by Christians doesn't preclude a Norse mythological motif though; again, these stories were not necessarily viewed as being intrinsically linked to pre-Christian religious practices. They were not scripture).

The internet will happily sell you a pendant with tons of 'Norse' symbols on them though. These are often either not from the Viking Age and/or their meaning is made up and prominence is exaggerated. The only symbol or talisman that was both popular in the Viking Age and has a definite connection to a god is the Thor's hammer pendant. Beyond that there really isn't a sophisticated or clear-cut religious iconography (which is why people seem intent on inventing one).

Brink, Stefan; How Uniform Was Old Norse Religion?, 2008

Bäck, Mathias; Hållans Stenholm, Ann-Mari; Ljung, Jan-Åke, Lilla Ullevi - historien om det fridlysta rummet : Vendeltida helgedom, medeltida by och 1600-talsgård : Uppland, Bro socken, Klöv och Lilla Ullevi 1:5, Jursta 3:3, RAÄ 145 : arkeologisk undersökning, 2008

This is a recurring theme which has an unfortunately unsatisfying answer: we really know very, very little about actual early medieval Scandinavian religion, religious practice or mythology. With a dearth of literary sources from pre-Christian Scandinavia, the vast majority of what pop-history thinks it knows about Norse mythology is taken from sagas and works like the Prose Edda, but these were written up to centuries after the conversion to Christianity, by Christian writers and almost certainly with a Christian moral perspective in mind. Genuine works of anthropology from the period are few and far between; Thietmar of Merseburg springs to mind, but even his relatively balanced investigation of Wendish ritual is prefaced with a disclaimer that these rites are empty and the beliefs fruitless. While the sagas may have been based on oral traditions, we have to be aware that they would be the equivalent of us trying to write a history of the American War of Independence today based only on stories handed down verbally by people who may never have left Vermont in several generations.

The truth is that many of the gods named in the sagas which have filtered into pop culture as being the leading figures of the Norse pantheon appear either very fleetingly or not at all in the toponymic or archaeological record, while many gods named in devotional wares, inscribed runes or placenames are absent entirely from the written mythos. Loki, for example, doesn't appear at all, yet pop-history holds him as a cornerstone of Norse mythology. We also need to beware that just because a particular god is mentioned in a specific work or context does not mean that they were universally popular across Scandinavian society as a whole. There are some contemporary works which purport to illustrate Norse religious practice but these are far from reliable. The most famous is Adam of Bremen's account of sacrificial groves to Thor and a giant gold statue at Uppsala, but this has to be judged against the context of much of Adam's supposed anthropology of the Baltic being lifted almost verbatim from Pliny the Elder's Historia Naturalis, containing wonders such as Amazons, Cynocephali and Blemmyæ. Certainly we cannot say with any certainty that the mythology we think we know about early medieval Scandinavia is accurate, or that we can give any real information as to how gods were honoured.