Cambridge has relatively good rail links to the rest of the UK. There are direct services to London Kings Cross, a slightly slower service to London Liverpool Street, Peterborough (for the north), Birmingham and Norwich.
When you arrive in Cambridge you will find yourself at Cambridge railway station which is on the edge of the city centre - details below. Journey time from London Kings Cross to Cambridge is about 50 minutes and from London Liverpool Street it is about an hour and a half - both services are subject to delays and cancellation. Make sure you don't catch the local stopping train to London Kings Cross which takes an hour and a half!
The main points that lets the rail service in the area down are the cost of rail fares, the rail services operated by Abellio Greater Anglia and that there is no regional integrated travel card.
This is the official journey planner for the UK's rail network. It also features 'Live Departures Boards' which are useful for finding out in advance if your train is running late or from which platform it will depart from. The website doesn't sell tickets but links to other sites that do.
PlusBus is a cheap bus pass that you buy with your train ticket at any National Rail station ticket office or online. It gives you unlimited bus and tram travel (on participating operators services) around the whole urban area of town.