The short answer is that you need to try different weights in order to figure it out. Even if you were to work with a personal trainer, the same process would be required. There is no perfect system for figuring out the amount of weight for a given exercise that you’ve never done before.
If the target reps are 15 reps for a given exercise, then your first set you get to 15 reps. You could only do max 1, or 2 more reps (16, or 17) if you kept on going. This is called training to failure. On your second set, you may only get 13 reps, and the last set you may only get 11 reps. If you get 15 reps on all sets, you should increase the weight. The goal is to try to increase the weight and make the exercises more difficult over time.
Here’s some more specifics –
Full Body A
1A) Squats with exercise ball = No weight on first set. If too easy, then go to 10lb dumbbells. If too easy then go up 5lb increments each set.
1B) Forward Lunge – No weight, if too easy, then go to 10lb dumbbells, go up 5lb increments on subsequent sets if still too easy.
2A) Flat DB Bench Press – start at 20lb, then go up from there
2B) Single Arm DB Row – start at 20lb – then go up from there
3A) Seated DB Shoulder Press – start out at 15lb, then go up from there
3B) Knee Crunches – No weight with this one