Eurostar arrives in London at St Pancras International. When going to Cambridge, one must go to Kings Cross, which is 1 minute walk from St. Pancras (St. Pancras Eurostar to King Cross platform 0 are about 10-minute walk away.) When exiting from Eurostar platforms and arriving in the main alley of St. Pancras (plenty of people, a Mark&Spencer and lots of other shops), take the right as the signs say (follow "National Railways", as Cambridge is in the same nation as London). At the end of the straight alley, we can see the exit to Kings Cross, it's about 50 meters aways (just cross the street carefully, there are crazy drivers in London, just as in any big city).
London — Cambridge off-peak with return : 33.50 pounds (return in less than a month). About 10 pounds less when return is the same day! (basically, return is almost free when on the same day). And of course, if you're not planning to return within the next 4 weeks, don't take the return option.
Different companies for trains: it doesn't matter. Railways and stations are common. Tickets regularly bought at the train station are valid for any train making the journey as indicated on the tickets.
Some machines are credit/debit/payment cards only, a few accept bank notes and coins. You should go and interact with a human when in need of information.
Generally it's a lot better to take a direct train from London to Cambridge (no stops in between). Usually there is one that leaves 15 minutes after one that stops at many stations, but takes 15 minutes less! So they roughly arrive at the same time.
Trains are not infallible: sometimes they are late. (They are either on time or late, if they are early then they wait on the platform.)
The ticket is generally mandatory to exit a station. If the ticket is the first part of a trip with return, then it's kept by the machine.
If you need a receipt, don't forget to ask the machine or the human, they can give you that.