Tipping is pretty much expected at the end of the climb, and the amount can be non-trivial so make sure to budget for it. Some operators are more formal (they give you a piece of paper to fill out how much to tip and an envelop to push money in), and others are less formal (where you just give cash out)
The customary amount is largely fixed on a per-day basis, varying by the position. Here's some info I came across before I went and it was largely accurate for me (apparently this amount is based on the guidelines published by an independent NGO called Kilimanjaro Porters Assistance Project)
The lead guide (1 per group): US$20 per day
Assistant guide (1 per 3 climbers): US$12 per day
Cooks (1 per 10 climbers): US$12 per day for each of the cooks
Porters (varies by route but the number can be large, i.e. >10): US$12 per day for each porter
It works out to be that the smaller the group size, the bigger the tip amount per climber. If you're climbing in a group of 6 or fewer, you can pretty much expect to tip over US$300 for 6-day trip, more for longer
I was in a pretty large group we had 15 climbers. So each of us only tipped around $170
I tipped in USD. Some people from my group tipped in Tanzanian shilling
You should probably double check the expected tipping amount with your tour guide before you book. Some guides might try to inflate the tipping amount beyond the customary amounts