A guarantor is someone who has agreed to pay the rent if the tenant fails to, for whatever reason. Depending on the Agreement, which must be in writing, the guarantor may also be responsible for other conditions under the tenancy, for example any damage caused at the property.
You will need to reference check the guarantor to make sure that they can afford to pay the rent in exactly the same way that you would reference check the tenant. I would suggest that the guarantor should be a family member (mother/ father/ brother etc.) not a friend or previous partner, for example. The guarantor should also be a UK resident so that, if required, you would be able to instigate legal action against them.
You should write to the tenant's guarantor explaining their responsibilities and enclose a copy of the Tenancy Agreement before the tenant signs it.
During the period of the tenancy it is important to keep the guarantor informed about any issues, particularly rent arrears, so that they can take action to resolve any problems and minimise any potential losses.
Finally, do you actually need a guarantor?
Well, the question is why has the tenant offered one in the first place? Do they have a poor credit history - any CCJs (County Court Judgements) or similar? Do they have a history of not looking after previous properties and/ or causing damage or noise nuisance?
At the end of the day it is up to you to judge whether you consider it necessary to have a guarantor. (It's worth remembering that very often con-artists come over as the most charming people you could wish to meet!)