Specific advice
OK, here's some suggestions:
1) I do a single card countdown.
Often we don't count cards singly, but in pairs, threes or fours. This allows us to cancel out a +1 card and a -1 card (for example) rather than incrementing and then decrementing our count. Obviously this is easier with lower-level counts. You can try turning over multiple cards at once, or better still just thumb through the pack face-up while keeping the count. Another trick is to remove one or two cards from the deck and then work out what they could possibly be afterward.
Strive for accuracy as well as speed, but it won't matter in actual play if you are out by one or two occasionally.
2) I play some blackjack with myself and 3 other pretend players. I focus on keeping the count and playing BS on all hands.
Get some chips and practice betting and paying off the hands as well. You should always check that you have been paid off correctly - one missed payoff can wipe out your edge, and one extra payoff can greatly enhance it. ;-) Plus if things don't work out you'll be able to get a job as a dealer. :-/
4) Lastly, I use the software Smart Cards and practice the count on it. There are many different patterns on this software. But they don't have a pattern that simulates exactly the real thing in Casinos.
I haven't used Smart Cards, but like just about everyone else I recommend Casino Verite. You can get it at www.qfit.com. As well as simulating live play, it also includes special drills for sharpening many of the different skills you need as a counter.
Hope this helps.