How long do I have to use the resin I've mixed?

That depends on the project you're making.  Once mixed, and allowed to rest for 5 minutes, here are the windows you'll want to work within:

Casting with photos/other flat paper - pour the resin into your molds right after it rests, get your photos in while it's as liquidy as possibly, so bubbles have the best chance to rise and pop.

Casting with loose elements - add resin first, then add elements, your resin will be workable for up to 20-30 minutes after resting.  Even if it thickens up, as long as your elements aren't really porous (bubble-making), you still have time to add things. 

Layering in molds - allow each layer to set up for at least 3 hours before pouring next layer.

Doming - you can apply your resin right after the 5 minute rest period, or let the resin thicken for up to 25-30 minutes.

Varnishing - best applied by pouring, or spreading with mixing wand, right after rest period, or up to 20 minutes after mixing.
Repairs - you can use your resin right after the rest period, or you can let it thicken 1-2 hours to use to create thicker bond.