There are two reasons why Im asking this:

1. I watched a video by a fitness instructor who discussed how some people warm up by lifting weights and when they get upto a useful weight which is able to build muscle the person is tired because the the weight they used to warm up where to heavy .

2. the weights I have are 20lbs I dont feel there doing me much benefit and Im looking to buy heavier weights

But the questions is is there a method of deciding which weights to use. For example, lets someone walked into a gym for the first time how do they know to use 10lb weights many time or use 20lbs and soon move onto 30lbs?

Trial and error. Of course if your new to lifting you'll start very low and work your way up. If you try 10lb weights for an exercise and you're not feeling much fatigue after many reps, try 15lb weights.

1) you can warm-up and stretch with weight, and that should be a short set using very minimal weight, to prevent the fatigue. You simply want to get some blood flow to the muscles you plan on working. I do it. I'll warm for a bench after first enerting the gym. I usually rep 165-185lbs on the bench, but before that I will do a set of 8 reps with 110lbs.

2) If you have one set of dumbells, you are severly limiting yourself to the exercises you can perform. Ideally you should join a gym, but if you're not going to do that, you should pick up a complete set weights. That way you can see what weights you'll use for certain exercises, and then when you get stronger you can just move up a weight set.

I am planning on rejoining a gym, the weights I have are pretty good and can be adjusted to a number of different combinations.

How heavy are you DB's? and like what has been said, id either try get some more weights/equipment or join a gym if your wanting optimal muscle growth you should be doing between 6-10 reps each set making sure that the final rep(s) really do push you to your limit.

Adjustable dumbells?

I do dynamic stretching (focus on hips) prior to any lifting. Then Ill work up to my working weight.

For instance: 1@135, 1@185, 1@225, 1@245, then lift
Those are large increases since it is for deadlifting. For upper body, the jumps may only be 10-20lbs.