I gave both to my baby bun at 7 weeks. More alfalfa than timothy to begin with, then equal amounts, and now I have him eating just timothy grass hay - he's 8 months old now. It was a very gradual change.
I gave him a fresh handful of hay twice a day. You could do 1 big pile daily. I also have a metal hay rack where he can eat hay from if he felt like it. Usually I just stuff the rack full to the top and then I take a bunch and put it in his litter box so he can easily eat it.
When to take it away? I clean out his litter box where I put his hay every few days so it all gets thrown out at that point. But pretty much, expect that the bun wont' eat it if they've pooped or peed on it. Then they need a fresh batch. Eventually you get an idea of where their "poop" and "pee" spots are and so don't put their hay there. Some bunnies are very picky and wont' eat some of their hay "just cuz". If you find that they are not finishing the hay you give them and they haven't peed on it, then they must just be refusing to eat that pile for whatever reason. DOn't leave it there thinking they'll eat it later. If you find the bunny being choosy, it would be best to give them more so they can continue to eat. Unfortunately many bunny owners end up wasting hay because of choosy bunnies but they have to eat so I end up using some of the "extra" as litter sometimes.