You are probably best with the hammersmith and city line, the circle line is plagued with problems.
From paddington train station, follow signs to the "hammersmith and city line". You want EAST BOUND, towards Barking (I think this is right, if my tube memory serves me correctly), when you are on the train you will see a map above the window, the train stops at every station, you can count the stations down to your station, get off at Kings Cross St Pancras and follow signs for "Trains".
Once at Kings X you will see a massive departures board, you are looking for trains towards peterborough or cambridge usually. Any train that stops at Hatfield is fine.
Let us know how you get on!