Effect (player) (effect) (time) (strength)
The potion effect strength can go as high as 250 but by then it usually cancels itself out, so control MATTERS!
/effect <player> <effect> [seconds] [amplifier]
Effect number list (Add this to the <effect> section)
4 Mining Fatigue
6 Instant Health
7 Instant Damage
8 Jump Boost
12 Fire Resistance
13 Water Breathing
16 Night Vision
21 Health Boost
So if you wanted to add speed to the player, you would do this:
/effect <Your Name> 1 <number of seconds> <what level of speed you want>
If you have a server, such as RPG or fighting, or arcade,
you can use command blocks (ID 137) to give people potion effects for certain situations.
If you have cheats enabled you can obtain command blocks with the following: /give (player) 137
More on this complicated topic:
Thanks to simonh2000 for putting this together!