I've been running for a little bit now. Every time I seem to try to increase my distance I get hurt. What is the correct way to do this to avoid injuries?
Building base is hard.
Everything depends upon the base. Getting a base going is hard, and often involves injury. Once you get past that, people often (always exceptions, there are no hard and fast rule) start getting a different class of injuries, usually due to overwork or imbalances that show up at higher intensities.
So you need to do as much as you can without getting injured, and slowly increase. That old 10% rule.
Your injuries might be due to biomechanical issues. Proper shoe selection might help. Orthotics may help. Strengthening excersizes to overcome muscle imbalances may help.
But there is no silver bullet, other than to proceed cautiously. Do not try and run through something that hurts, consider it, and make a wise choice if it something you can run through or not.
As a side note, this is why you NEVER want to stop running for several months! You lose most of your base and have to start again. That sucks. A lot.
First of all, the 10% rule, only increase the mileage of the week no more than 10% than previous week;
I would also suggest that do not increase the pace/speed and distance at the same time, either increase the distance while maintaining or even at a lower speed than previous distance run, or increase the speed and do not exceed the distance of previous run;
For injury prevention, however, you have to first identify the kind(s) of injury and find the correct way to prevent it. Personally I find the book "Running Injury-Free" very valuable resource;
Weight training is important, it helps strengthen your body core so you can keep the right running form during distance run, but also builds up supporting muscles and thus minimize the risks of injuries;
Other important notes: proper hydration and proper running shoes for the training types, do not run on hard surface like concrete pavement for too long, do not over-train, etc.;