How do you start dog walking?

You will need insurance
A canine first aid qualification would be advisable (Canine First Aiders provide the only nationally recognised qualification in the UK)
Join a professional body such as NARP

One thing I’ve learnt – Don’t buy a franchise!  🙁
In my experience (I’ve been doing it for 4 years now and making a reeeasonable living), going out to parks in the areas you want to walk dogs early in the morning and late in the evening (when people are walking their dogs before and after office hours) and chatting to people is the best option. Postcards in petshops and vets, shops… best advice though, is to get a really good web presence… make a proper website and get on Google, etc… People always look online first!