This is closely related to what Prison Category the person is allocated.
After someone is sentenced (whether they were on remand or on bail) they will normally go to their ‘local’ prison. If the sentence is a short one (typically under six months) then it is likely that they will stay at that prison for the whole of the sentence.
For longer sentences, there are various factors set out in the Prison Service Orders in deciding which prison someone will got to. There is no legal requirement for a prisoner to be allocated to any particular prison, or a prison within a certain distance from their home. However, the authorities will try to put someone who is serving a longer sentence close to their family if possible. Family ties however will not generally impact on prison categorisation.
Prisoners can be (and often are) moved around during their sentence for similar reasons as their initial allocation. A prisoner can request a transfer for family or other reasons (or because they are having difficulties, such as being bullied, at the prison that they are in) and this will be considered by the Governor of the prison that they are in. There is a general lack of resources in the prison service, so even if the Governor is amenable, it may not be possible. If a request is refused, then the remedy would be a complaint to the Prisons Ombudsman or a Judicial Review. Given the wide discretion that the prison service have, it is extremely difficult to win a Judicial Review however.
If you are looking to find a prisoner, then you can contact the Prisoner Location Service. For obvious reasons, they will need to speak to a prisoner before passing on to.
Official information on what happens when someone is processed (when they first arrive in prison) and prison life in general can be found from the Prison Reform Trust. An unofficial guide (one person’s experience) can be found here.