How do you put a soft carrot in your butt?

Generally, it's not a good idea to put things like this in your anus. Anything you put in your anus should have one end that won't fit in -- a base, handle, or something like that. The anal muscle might suddenly contract and -- if you don't have a good grip on the carrot -- actually pull it all the way in. The bad thing about that is that the large end of the carrot usually has the remnants of the carrot stem on it, and they can be rough. That makes it very painful to get the carrot out. People have wound up in hospital emergency rooms because they put the wrong things in their butts.
Since the anus doesn't produce its own lubricant, anything you put up there will need to be lubricated. You can buy sexual lubricants at adult toy stores and most larger drugstores.
Go slowly -- if it hurts, you're doing something wrong.