That's not so hard as it sounds. By a wonderful coincidence trains which are headed via St Pancras from Gatwick to Cambridge stop at St Pancras International which is the London terminus of East Midlands Railway which shoots up north right to Sheffield.
St Pancras International is an interesting station. Nearly demolished and abandoned, the station was saved after a public outcry let by the poet John Betjeman. It and its companion building of the beautiful hotel which is now operated as a Marriott Renaissance, are true iconic buildings. They are next to Kings Cross station. Apparently St Pancras has the longest champagne bar in the world. whoopee.
Trains from Gatwick, in fact all Thameslink trains, arrive under the station in an underground tunnel. The platforms are reachable by a double set of escalators and two sets of lifts. The Thameslink station is in the top left of the station. Directly above it, also served from the main concourse by lifts and escalators is the station for East Midlands Trains.
In the top right, upstairs, is the station for the Javelin high speed trains of Southeastern which run on the HS1 high speed line to Canterbury, Stratford (not Shakespeare), and many parts of Kent. It is the same line which Eurostar use for their trains to Paris, Brussels, Lille and Amsterdam.
Speaking of Eurostar, their station is in the middle of the concourse, about half way between the tube station (and hotel) and the other stations I have just mentioned.
So those are the main services at St Pancras. Each railway gets its own part of the station, but it is well integrated and flows very well. The live piano music (available to all to play the pianos) is usually pleasant, and the station is light and airy.
Oh, and the food. There are all sorts of food outlets in the station. Pretty much everything you can imagine. If you don't like the selection there, just cross the street into Kings Cross and they have even more. Even a supermarket.
Also shops. Books, Boots, coffee, toys, Belgian chocolate (Godiva), magazines, clothing - you name it.
Boarding the train to Sheffield is easy - you need your ticket for the barriers, and then the train is directly ahead. Sometimes they stack the trains so your train may be further along the platform than another train which follows you out of the station. Just read the notice boards. Staff are in easy to spot distinctive uniforms and will help you.
There is a train every half hour to Sheffield, at xx:31 and xx:02. The 02 train is a little faster, just 11 minutes, but that is so close to not make much difference.
The xx:31 usually calls at Leicester, Loughborough, East Midlands Parkway, Long Eaton, Derby, and Chesterfield (see if you can spot the crooked spire) on its way to Sheffield. Takes about 2:10. The xx:02 only calls Leicester, Derby and Chesterfield and is 11 minutes faster.
The train station at Gatwick is directly under the South Terminal, lifts and escalators.
I don't think we know when this trip is - day of the week, arrival time at Gatwick. It might help answers. Oh, and next week or next year?