Its pretty simple- but you do need a solicitor. Well I suppose you could try and diy but that would not be my recommendation.
If there is a mortgage, you will need to join the lender into the deed - thats a bit painful as the lenders are sort of reluctant to get involved in what is a tedious process for them. Often, people do the transfer when remortgaging - that is much simpler. There are no stamp duty or tax implications and there are no registration fees because its the transfer of a family home.
mf