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If I list my home and hang a sign out 'for sale by owner', and a realtor brings a buyer in, who wants to buy it, who's going to pay the realtor?

I did not hire him, so I don't want to pay for him. The buyer will assume that it is covered with his sale price (because I, the seller, normally get less than that).

I can imagine, the realtor gives me a reduced offer price, so I never see the share that goes to him. is this how it usually works?

In other words, if I get an offer for X, and I accept it, can I assume I get the full amount of X?

State: FL

You negotiate with the buyer's realtor, just like a seller's realtor would do. He already has a contract with the buyers that says he won't charge them a commission. He will have to get it from you. You will tell the realtor his clients will have to offer more to cover his commission, and he will resist. And eventually you will either agree a price and a percentage, or his buyers will walk.

Some jurisdictions have laws that restrict the criteria on which you can decide between competing offers (generally to prevent racial discrimination). I don't know if you're supposed to consider your net after the realtor's commission in such places, or if you have to compare the two offers on the top line price.