You can use a name generator or just make them up yourself. One thing that bethesda does often for city names it to take two words and push them together, i.e. Elder Root, Highrock, Hammerfell, Black Marsh, etc. For city names, think about the suffixes that they usually have(burgh, sted, hold, helm, mouth, and ford to name a few). As for naming months, I'd probably just wing it but you can try and pick apart what TES did for their month names.
Also what about coming up with words? like names or country names or even days of the week or month? how would you go about with that and not make it sound really stupid?
How I usually start forging a world is I picture in my head what kind of world it will be, and then take a pencil and draw a first draft of a map. I'll work off of that for a while and then probably redraw the map with more/different/less cities, more interesting features, more natural transitions, etc. I generally figure out what I'm doing for races fairly early on as well.
After I have some basic nations with their conflicts, cities, setting, and gods, I'll usually start mapping out their more intricate lore(origin, heros, factions, etc).
I'd say you can pretty much do this however you want. If it helps you, make a timeline. I personally love geography and history, so for me making a map works pretty well.