This varies so much from publisher to publisher. Ask yourself, are you in it for the money or just the pleasure of seeing your work in print. Most of us, realistically, want both, and it is possible to make a living at this.
Punchlines require a special skill and earn more - up to £150 per idea. Verses are usually paid by the line or a one off fee is offered. This can be 50p per line to £25 per verse. Some humour publishers pay according to how many jokes you have had published by them. Eg. Your first ten acceptances may earn £100 each, your next ten may go up to £125 and when you have had twenty published in one year your fee could rise to £150. There is money to be made here - but you have got to be good!
Most publishers purchase work outright and you instantly lose ownership of the copyright of that piece. Some, however, do pay royalties and others are willing to negotiate either way. If they wish to publish your work it is worth asking about this.
Once your work is accepted, you will probably be asked to send an invoice. Writing is a business, you are generating an income that must be declared. It is advisable to enquire with the Inland Revenue to see if you need to pay tax on this income.