Just to add to @dumbcoder's answer sicen you asked for specific advice
St Pancras International is on three levels. When you arrive on the Thameslink you are on the lowest, below ground level. Take the escalator or lift to the exit. Keep your ticket handy to operate the gates. There is a wide gate if you have a wheelie bag with you, I think it is to the left. When you exit the gates turn left and you will see the exit you need on the far side of the concourse.
When you exit STP you cross the road and you are in King's Cross station. The departure boards are in front of you. Beyond them are the low-numbered platforms from which the long-distance trains depart. To your left is a smaller block of platforms from which, I my experience, the trains to Cambridge usually leave. I say usually.
If you want to buy a sandwich or get a coffee you are better off to do it at STP, you will already have noticed the shops to your left as you walked through there. You can do this at King's Cross but most of the outlets are on an upper level with escalator. There are free toilets at STP (which is unusual in a British mainline station) but they are up two irritating small steps which impede wheelie bags.
It takes about 2:20 according to the National Rail website.
Edit 27 February 2018
With the opening of a connection between Thameslink and the East Coast Main Line there is now one direct train per day between Gatwick and Cambridge. It currently leaves at 1203 arriving 1414