How much to increase weight by?

When it is time to add more weight when weightlifting, how many pounds should I increase it by?

Or what it be determined by how many reps I can lift with the new weight?

There are probably a lot more qualified people out there to respond to this, but my understanding is that if you can do more than 12 reps in a single set with a given weight, you need to increase the weight.  This is assuming that you're working under the low rep, high weight theory of lifting, but most people who seriously lift weights follow that line of thought. 

As for how much of an increase, it depends on where you're at and what set of muscles you're working.  For example, if you can do 3 sets of 15 reps (3x15) of a squat at 100 lbs, you might increase your weight 10 lbs or so and see where that leaves you.  If you can now only do 3x6 reps, you're probably at the right weight.  If you can still do 3x12 reps, you might increase the weight even more.  However, squats target the largest muscles of the legs and you're starting at a higher weight, so increasing by 10 lbs is only a 10% increase.  For an exercise that targets a smaller muscle where you're already using less weight, you might only increase the weight by 5 lbs or even less.  So if you're doing shoulder presses with 10 lb weights right now, and you can do 3x15 reps, you would probably only increase the weight to 12 lb weights and see where that leaves you.  You're now using a weight that's 20% heavier!  But as you can tell, it's a bit of a trial and error process.

A ten percent increase, or as close as your equipment allows, is best for safety. If your can still do the same amount of reps and sets, bump up another 10% next work out.