I'm not quite certain what you're asking here, because 'modern' is something of a fuzzy term in culinary history - with the exception of the microwave, there's very little you can do in a modern kitchen that wasn't done in Babylon or Eygpt.

All the processes you're asking about have been around since before anything about cookery was written down - this is clear from archaeological finds. Indeed, use of fire for cooking may predate homo sapiens as such, as detailed here in Discover: http://discovermagazine.com/2013/may/09-archaeologists-find-earliest-evidence-of-humans-cooking-with-fire

For written records, De re coquinaria, attributed to 'Apicius', is the earliest currently known European cookery book, compiled in the 5th or 6th century. It has recipes that you could use today:

"Hot Kid or Lamb Stew. Put the pieces of meat into a pan. Finely chop an onion and coriander, pound pepper, lovage, cumin, liquamen, oil, and wine. Cook, turn out into a shallow pan, thicken with wheat starch. If you take lamb you should add the contents of the mortar while the meat is still raw, if kid, add it while it is cooking." ('The Roman Cookery Book', 1958, trans. Flower and Rosenbaum, pp. 188–89.)

There's also the Kitab al-Tabikh (basically, 'cookery book', more literally 'book of dishes') by Ibn Sayyar al-Warraq, which lists recipes, medicinal and culinary theory, history, and poetry from 10th century Baghdad - I've cooked a good few of the recipes from it, from sandwiches to stews, and they're all good.

To answer the particulars as best I can:

[W]hen did things like oil and salt become standard?

Both predate any written history.

Did people used to fry meat or was baking the normal standard?

Both have been done for a very long time. Roasting was probably the first form of cooking, where meat is cooked in direct heat from a fire (but not usually above the fire, as you'll see on TV - that leads to charred meat on the outside, and raw meat on the inside). Frying can be done on hot stones. Baking requires an enclosed space, but again, that can be made from clay and stones. Indeed, many modern pizza ovens are essentially like that.

Salt is now considered a crucial ingredient in food, but at what point did salt become that way?

Salt has been around for so long and in so many parts of the world that I think 'always' is a reasonable answer here. It comes just after water on the Food Timeline: http://www.foodtimeline.org/

Did people used to substitute salt for other spices?

Do you mean, did they use salt when other spices weren't available? Sure, but there are almost always herbs and spices available in some form, which are added to foods to vary taste.

Also, what do we know about how recipes and ingredients were spread and integrated into the local cuisine?

This is a whole area of study in and of itself, which becomes easier the later in history you go. New World ingredients (tomatoes, potatoes, chillis, etc) being brought to the Old World is probably the clearest example, but there are plenty of earlier ones - the Romans brought rabbits to the British Isles, for instance. By and large, recipes and ingredients spread with cultures, so following invasions or migrations.