As said above, go to www.nationalrail.co.uk and put from GTW to CDF and find your date and estimated time of departure. You will then see cheap fares of around £20 for advance booking specific trains. This involves going from Gatwick to Reading and then changing for a train to Cardiff. This is much easier (& cheaper) than going into London & having a journey on the underground to Paddington station (from Victoria). Gatwick to Cardiff will take around 3 hours 20 minutes. (Cheaper fares will not be available during peak commuting times). The London to Cardiff railway is being electrified. Diversions may take place - these are most likely on Sundays.
Once you have found your desired service, pre-book (like 10 weeks ahead if possible) with the Great Western Railway - for it is their trains that you will use throughout this journey. You will get a booking number - I would print this off to take on your trip. On arrival at Gatwick station, insert the SAME debit card into a ticket machine and type in the booking number and out will come your tickets. (You make also be able to go to a member of ticket staff at Gatwick to claim your tickets).
In the event that you are early and catch an earlier service, find the guard for the earlier train - usually at rear when in stations - and ask if you could take his/her train without penalty as you landed early.
You might like to go to the Wales forum and check posts about Cardiff.
