Getting results with a mediocre team

Say I have to do a project with a team of quite mediocre programmers. Some of them are older but rather slow, and some of them are fresh out of university and not very experienced. The code they produce usually works (but sometimes not), but is poorly documented and very hard to maintain. Also, the development process is very slow and we have a lot of bugs.

However, I have to do the project with this team, as neither time nor budget allows to add or replace team members.

What are best practices to manage a team of only mediocre developers? How can we speed up development and improve code quality? How can I foster learning between the team members when there is a problem no one knows how to solve?

I'd also be happy about book recommendations which cover this topic.