There's no real limit to how many you can undertake at once. My advice would be to always complete the quests you have acccess to inside one area before moving on to the next area. This way, you'll never get overloaded by quests. The questline is actually very well structured so if you follow the main story, you'll visit all of the world and be exposed to pretty much all of the sidequests.

Also, just hit 'J' to bring up your journal if you want some info on quest objectives for a quest that isn't on your main screen.