How often should I go up in weights when training?

If you're focusing on strength, then you should be working with heavier weights at lower rep counts. With that assumption, I'd suggest increase weight when you can complete more reps than is necessary for your strength goals.

MFP will have you believe that rep counts for strength vs size vs endurance is black and white. It's not. So it's kind of up to you. If you can complete 8 reps for all sets and want to increase weight, go for it. If you want to wait until you can do 12 or 15 reps for all sets, that's fine too. I would lean towards the later, personally.

ETA - a good program should include when to increase weight and by how much. If you're doing a established program, double check it's recommendations.

You should either consult a personal trainer who will design a program for you or consider one of the "off the shelf" options (like StrongLifts), and then follow the recommendations.

I don't lift heavy. I do dumbbells up to 2x15lbs now. I started with a book that gave initial sets and reps. Something like:

Front squat with weights.

Level 1: 10 reps, 2x3lb dumbbells, 1-2 sets
Level 2: 12-15 reps, 2x5-8lb dumbbells, 1-2 sets
Level 3: 8-12 reps, 2x10-12lb dumbbells, 1-3 sets.

So, I made up my mind that every week, I'd try increasing... something. If I couldn't do it, I'd stay where I was for another week and try again. So, for me, it kind of went:

Week 1: 1 set @ level 1
Week 2: 2 sets @ level 1
Week 3: 1 set@ level 1 and 1 set of 12 reps with 5lb dumbbells (i.e. lowest setting@level 2)
Week 4: 2 sets of 12 with 5lb dumbbells
Week 5: 1 set of 12, 1 set of 15
Week 6: 2 sets of 15
Week 7: 1 set of 15 with 5s, 1 set of 12 with 8s

And so on...

When I got to the top of level 3 (i.e. 3 sets of 12 reps with a pair of 12s), the following week I did two sets with the 12s and then my third set was 8 reps with a pair of 15s.

At some point, I am going to join a gym and get a few sessions with a personal trainer, but so far, this has been working. Of course, I just had surgery last Thursday and now I'm not allowed to lift more than 3 lbs for the next 2 weeks, but my doctor is referring me to a dietician so that we can figure out what kind of strength training I can do while I heal.

I do a program called "Body for Life" by Bill Phillips. You can order a used copy on Amazon for really cheap. It's a 12 week program. If you follow the diet and exercise you'll get guanteed results in strength, plus weight loss if you need it. He ecplains everything you wanna know, including increasing your weights. My favorite part is i get a free day once a week. Makes it so easy to stay on track. There are food lists, charts, and exercises, all in one place. I highly recommend it. I still log on mfp just so i can see my progress and keep track of my food.

5 more pounds on Monday.