Whether you're using a contractor or doing the work yourselves, you need to keep an eye on a few things whilst a path is being built. Most importantly, you need to make sure that the people building the path and anyone passing by are kept safe. Many people are familiar with the idea of following health and safety guidelines, but there are some specific rules which apply to construction projects which you must be aware of - you can find further information on those rules here.
You also need to keep local people informed, so they know what's happening. It's worth telling your funders that construction has started, so they know what's going on. If you're working on any path, you'll also need to discuss with your local access authority whether or not it's appropriate to close the path whilst the work takes place.
If you're using a contractor, you need to make sure you're following good practice in terms of managing the work that they are doing - don't just hand over your specification and walk away. There's more information on working with contractors here.
There's a lot more information on path building in the Lowland Paths Guide, which you can find here.