Hi,
I have done this previously for my own logo and clients.
You need to know whether this will be TM for UK/Europe or rest of the World.
If it's a TM for UK/Europe then you need to understand the class that the client sits in based on service provision (see
Intellectual Property Office - How we classify goods and services for classification guide).
Once you know your class you can then complete the IP form for registration:
Intellectual Property Office - On-line form TM3. Here is a list of associated fees based on cat type:
Intellectual Property Office - Trade mark forms and fees
There are many companies online that offer TM services; however, I think you will find that the ipo.gov.uk site is the most reputable and reliable for TM registration.
Hope that helps.