Sorry for short answer, I hope someone with or insight will help you...

First there was the Volga trade route, Varangian merchant traveled down the volga river to the caspian sea and traded with the local khaganate or even choined caravans to Bagdad

"Ibn Khordadbeh" a persian schoolar wrote a about north european merchants visiting Bagdad:

"[They] transport beaver hides, the pelts of the black fox and swords from the farthest reaches of the Saqaliba to the Sea of Rum [i.e., the Black Sea]. The ruler of Rum [i.e., the Byzantine Empire] takes a tithe of them. If they wish, they go to the Tnys river [i.e., "Tanais", the Greek name of the Don River], Yitil [i.e., Itil, the ancient name of the Volga], or Tin [variously identified as Don or Seversky Donets], the River of the Saqaliba. They travel to Khamlij, the city of the Khazars whose ruler takes a tithe of them. Then they betake themselves to the Sea of Jurjan [Caspian Sea] and they alight on whichever of its shores they wish. ... Sometimes, they carry their goods from Jurjan by camel to Baghdad. Saqlab slaves translate for them. They claim that they are Christians and pay the jizya."

Second there was the "Varangian Guard" in the army of Byzantine Empire, a elite unit composed of Scandinavic and Anglo-Saxons. It wos formed in the late 9th century and lassted until the 11th century. But there were also earlier mentionings of varangian mercenaries.

Third, there was a islamic shoolar who traveld to the Volgo Bulgars/Volgo vikingsm and wrote about them: "Ahmad ibn Fadlan"

"I have seen the Rus as they came on their merchant journeys and encamped by the Itil. I have never seen more perfect physical specimens, tall as date palms, blond and ruddy; they wear neither tunics nor kaftans, but the men wear a garment which covers one side of the body and leaves a hand free. Each man has an axe, a sword, and a knife, and keeps each by him at all times. Each woman wears on either breast a box of iron, silver, copper, or gold; the value of the box indicates the wealth of the husband. Each box has a ring from which depends a knife. The women wear neck-rings of gold and silver. Their most prized ornaments are green glass beads. They string them as necklaces for their women. Ibn Fadlan, on the Rus merchants at Itil, 922." (Itil = volga)

Sorry for the missing sources but I think this is a good starting point for you.

wurzn gives you some good examples, largely textual, for contact. It is worth noting that we only have two direct "records" of Arabs actually reaching Scandinavia proper (as opposed to Scandinavian settled/influenced Russia and the Baltic coast), and that both of these figures came from Al-Andalus (Spain).

Aside from texts such as al-Ghazal's or Ibn Fadlan's, we also have archaeological evidence of contacts between Scandinavia and the Islamic world.

The primary trade site in Scandinavia proper (as opposed to Russia) where contact occurred was Birka, located about 20 miles west of modern day Stockholm. This was the premier emporium (trade port) in Sweden and has been extensively excavated and studied.

Finds include:

• Coins: The Numismatic's trail indicates a particularly lively amount of trade. Upwards of 85,000 Arabic (or Cufic) coins have been found in Sweden, some 700 in Norway, around 5000 in Denmark and a whopping 100,000 or so in Russia. The time frame seems to be roughly the end of the 8th century to the 10th, with the vast majority coming from the 10th. There is an abrupt fall off round about 1015. The majority come from Persia and the east, with a small number from Spain.

• Artifacts: We have a random smattering of miscellaneous artifacts, pots, metal work and some jewelry that originate in the east as well. This also includes textiles (esp. silk) from the east.

• Scales and Weights: Worth its own section, quite a few brass scales with lead weights have been found, some with arabic inscriptions, others without. This is useful for seeing both the importance of trade as a primary connective force and the influence of technology and tools from the Islamic world to Scandinavia.

As for influence, this is a much more complicated question. Coins and other goods often carry Arabic inscriptions (sometimes from the Quran) but the odds of Scandinavians being able to read them is pretty low. Certainly there may have been some attempts at conversion (just as there were Christian missionaries active in Scandinavia) but it clearly did not "take" as it were.

Sources: As always check out The Viking World if you have access to a library, there are several excellent short intro essays in there which can point you along your way. Ibn Fadln is translated if you want a primary source to read, though of course keep in mind that this is an outside looking in, not a Scandinavian centered perspective.

Happy reading!

In Inga Hägg's "Die Textilfunde aus dem Hafen von Haithabu," there are clothing fragments found in Hedeby harbor that may have been from something like a kaftan. Hedeby was located in present-day Denmark and abandoned toward the end of the 11th century.