As has been said, the Isle of Sheppey has little going for it. (we tried to put Sherrardk off going there four years ago - but she still went).
If you're determined to get there, simply find your way onto the M25 clockwise, go over the QE2 bridge, get into Lane 2 and follow the signs for "A2/(M2) Canterbury, Dover". (i.e. leave the M25 at Jn 2). The A2 becomes the M2, which you need to leave at Jn 5 (signed "A249 Sheerness"). That takes you straight to the Isle of Sheppey. The journey time from North London might be about an hour and a half.
As has also been said, if you're heading that way, Whitstable is far, far nicer. (Follow the M2 until it ends, then continue onto the A299. After 5 miles turn off, simply following the signs for Whitstable). However Whitstable isn't cheap. (B&Bs start from around £85 per night and you won't find any caravan sites, as you would on the Isle of Sheppey).
If you're looking for somewhere cheap, try Margate. Yes, it's also a bit of a dump but unlike, the Isle of Sheppey, it's got a lovely beach, some decent bars and restaurants (if you hunt around for them) and the Turner Contemporary gallery. It's also 'cheap as chips' for accommodation. (To get to Margate, proceed as above along the A2, M2 and A299 and continue until you come to the A28, which takes you into Margate).
Alternatively, head north up the A12 and come and see us in Suffolk. Southwold is the real gem but, again, it's pricey. Felixstowe is a rather pleasant town as well though and a great deal cheaper to stay in.