There are lots of simple options you can carry out to improve routes at the neighbourhood level. Just make sure you don't forget promotion too - simply having people use paths will help ensure vegetation does not cover them too much.
Map what's already there
First ensure all RoWs in your local area are included on OpenStreetMap - see the mapping what's in your area section. Increasing numbers of local authorities are making the 'definitive map' available as open data, which means it can simply be imported.
You should also try to add permissive paths that are not shown on other maps - this is a particular advantage of OpenStreetMap. Ensure you tag these correctly as permissive so that people do not get the wrong idea. Next consider adding surface conditons and barriers such as gates and styles. Besides being a handy way of recording where there are problems that could be tackled, this data is used in route planning services for people with different needs, such as walkers, cyclists and wheelchair users.
Monitor and maintain
Nature doesn't stand still. What might be easy to walk along one day could be near impossible the next month. It's not just a question of fallen trees and streams that have burst their banks because very occasionally landowners obstruct paths, though it is not usually deliberate. You could set up a parish linesman or footpath warden scheme alternatively you could encourage people to adopt invididual sections of route, something that Sustrans encourages for its National Cycle Network.
Spending cuts are affecting rights of way, with less money available for basic maintenance. CPRE Norfolk has launched a campaign to try to protect spending on rights of way and set up footpath wardens - see the Norfolk Protect our Paths case study for more details.
Improve existing or get new routes
Getting new routes (or at least permission for public access) can be as simple as negotiating with a friendly landownder. On the other hand getting new paths can be expensive and time consuming - negotiating to turn a railway into a greenway or getting a new path or walking and cycling bridge open can take years and cost at least tens of thousands of pounds. This is the focus of the step by step section.