There are many standard workout programs that use compound lifts, but I have yet to find one that uses dumbbells as default equipment. The reason is simple: A barbell would be just so much better. But I know you don't have one right now, so let's see how we can alter a simple all-compound programm to work with dumbbells.
For simplicity's sake I'm going to concentrate on the simplest workout program I know, which is Starting Strength. It consists of 4 compound lifts, that are doable with dumbbells to varying degrees. It looks like this:
- Squats: 3x5 (3 sets of 5 reps)
- Bench Press/Shoulder Press: 3x5, these should be alternated, so if you bench pressed last time, do shoulder press today and so on.
- Deadlift: 1x5
This should be done 3 times a week, as it's a full-body workout.
The above program relies on a barbell in its original form, so to use it with dumbbells some alterations will have to be made. I'll go from easiest modification to most severe.
Bench and Shoulder Press:
The bench press and the shoulder/overhead/military press can be done with dumbbells just as it can be done with a barbell. The side effect you get from using dumbbells, however, is a certain 'wobble' that you'll have to compensate. You will also have to use both arms independently, so you can't compensate for a weak arm with a strong one. Both side-effects may be viewed as beneficial, as the wobble increases coordination, while using two weights prevents muscle imbalances. Those side-effects will also make the lift harder to execute, form will be more likely to suffer and you won't be able to use as much weight. In general, you should be fine if you start slowly and work your way up as long as you use good form through all of your sets, on all of your reps.
The dumbbell squat is a bit more controversial, as the squat variants are very different exercises, depending on where you put the weight. Now you can't reasonably put it on your back when using dumbbells, so you'll have to find another way. I used to do dumbbell squats myself when I didn't have a barbell and found that I could handle them best with the weight on both sides. I just let my arms (with the dumbbells) hang and performed a squat. This worked for up to 88lbs (40kg) for me, before the weights hindered my range of motion. The dangers are leaning forward/backward to much and compensating with the dumbbells. Try to keep them beside you and don't move them back or forth.
This is the one lift most people wouldn't do with dumbbells, as I have often been warned. The regular deadlift is a very rigid motion and the aforementioned dumbbell 'wobble' would seriously compromise form. So when I started out, I tried the stiff-legged dumbbell deadlift, which requires a lot less rigidity. I managed to work my way up to 88lbs (40kg) with this deadlift variant, but could probably have lifted even more.
That's pretty much all there is to it. With the modifications mentioned above it should be possible to do an all-compound program with dumbbells only. While it isn't the most effective workout ever, it should be enough for a beginner to make considerable gains until a barbell becomes available. I myself did a very similar program for several months and progressed just fine, so it's not a two-week quick fix either, but can work for a long time.