One of the biggest disadvantages of non-SLR-type digicams is that the AF is pretty slow. in the range of about 1.5 - 3 (my exp.) Remember, digicams are but a tool, and the question you asked is a good question, but IMHO (no offense) i feel that the answers are technical and unless you buy a better, faster, much more expensive camera is not going to solve your problems.
I got a few assumptions to make when you ask that question. Firstly, is that, AF is a must, like when you are moving around looking for targets of opportunity. I'm talking strictly in slow AF here. If MF and your own reflexes allow you to be a one man AF system then go ahead. If you only can use AF, then this must be recognised as a limitation.
You might moan the countless opportunities wasted when the AF is too slow. Argh, blur! oh no, don't block the view! those kind of things. How I deal with it is simple - I don't let go of a subject. and I choose my subjects carefully. of course real fast action photography with a wide range of motion and distance (two kids in animal suits running around for example) your AF will have problems, coupled with the normally excellent DOF most digicams have, the AF will not work well.
So what I do is since I don't have to pay for film, I'll just AF, fire fire fire fire, AF again, fire fire fire, and sooner or later there'll be just this AF that works, and fire fire fire fire fire fire fire fire fire.
Remember, the greatest photographers have countless film rolls on hand. Darn national geographic lug around an icebox filled with film rolls on a day shoot. The animals moving, a cheetah bounding across, screw the AF. Just fire fire fire fire, AF, fire fire fire, then there'll be this perfect(or almost perfect, easily solved in PSHOP) AF focus, and the perfect composition, and the target is munching on a piece of chocolate bars after running around and getting tired. SHOOT!
How I deal with it is I explore a different avenue of photography. Focus more on your other factors that can be helped. Composition, exposure, contrast, range of colors and stuff.
You'll still learn, and when you get a good AF camera (please please let me strike 4D, just once! and the d1x is mine!!) then all these skills will be employed, then you can start brushing up on 'how to deal with a fast AF'.
Again, just my $0.02.
Yours,
Kelvin