In fact the sponsor for such a visitor would usually be yourself, if you are now resident in the UK. The letter is just needed as proof that your family member does have a relative who is inviting him or her to stay; they will still have to supply all the relevant documents to prove that it's OK for them to come into the country. You can find a sample invitation letter here; you can paste it and just adapt to your particular situation.
After that you could have a look at this website where you will find information on what to do next and what further documents may be needed. That should tell you all you need to know, but it is always advisable to look at the UK Border Agency website as well to make sure all your information is up to date; you can also contact them with any questions.