If you're training for performance, then the best way of measuring your progress is how your performance improves, especially if you're playing a team sport. However, many of you will be exercising to "get/stay in shape". Now this is quite a subjective term, so this means it is hard to accurately measure how your progress is going.
Many people think that weight is the most important, or even the only way of measuring your progress. However your weight can be deceptive. This is because, as you burn fat, you also will most likely build muscle. So say you lost 2 lbs since last time you measured, this might seem a little poor but you may well have lost much more than 2 lbs in fat but gained a lot of weight in muscle as well, this is also confounded by the fact that you lose a lot of water weight at the start, which is dropped quickly. It can be disheartening when you seem to have hit a wall in your weight loss; but while your weight may not have changed much, but the composition of your body has changed for the better.
This leads to what is probably the best numerical measure of progress, your body fat percentage. these can be found at most gyms as well as pharmacies etc. Now be warned, body fat measuring machines can lie. It may say that your percentage is higher or lower than it actually is. But do not worry, although these machines may be inaccurate they are very consistent. This means that, as long as you use the same machine, the change in your body fat percentage is very accurate (even though it will always over or underestimate your fat percentage as it is always off by the same amount) which is what you really want to be looking at. If your fat percentage is going down, that's all you need to worry about.
The next methods are somewhat more subjective, but they also give you more more insight and a better sense of achievement when you have made good progress. Firstly is how you feel, if you feel stronger, fitter, happier, more energetic or better in any way, then you're making good progress.
Finally, the most subjective but also the most satisfying way of measuring your progress, how you look. If people start noticing that you're getting slimmer or more muscular/ toned, then you're making great progress. When you look at yourself in the mirror, try to work out where you lose fat the fastest, or more importantly, where you start to put on fat first (although you can't control it you do lose/gain fat in different places at different rates). You should look at yourself at the same time of day and in the same mirror, as lighting and different mirrors can change the way you look significantly. It can be really great to use photographs to document your progress so you can actually see how much you've changed, which can make you feel a lot better, if that's what's bothering you.
So to summarise; your weight can be deceptive, just focus on the direction your body fat percentage is going, and if you feel and look better/ fitter you're making great progress!