There's all kinds of strenght training you can do without weights (though a pair of dumbells is like bare essentials, you can do almost anything with them).
Going with absolutely nothing, your left with push-up/sit-up type workouts. Obviously Push-ups and sit-ups are a good place to start (push-ups work chest and triceps). Since you have a chin-up bar, you can do chin-ups and pull-ups. That will work the latissimus dorsi muscle (mid-side back) and the biceps (though I think secondary).
After those two, you can do Hindu push-ups and Hindu squats. I've heard these generally work well.
If you can find something the right width, you can do dips, which will also work the chest and triceps. If you can, you can do bench dips, and then just weight yourself with anything heavy.
When you start to get strong, you can do handstand pushups. Basically, get two chairs and put them against the wall, then go into a handstand (on the chairs) and use the wall as supports and do push-ups.
6/18's will work your hip flexors and glute area. These are a variation of leg lifts, which if you can find somewhere to prop up with (same as dips situation) then they very important. Mountain climbers and the like are good as well.
Another good way to build strength is the lumberjack way. Get yourself an old tire and a heavy pole (bat with a donut on it, heavy stick, etc.) Now just chop on it like you would with an axe and log.
Generally, without weights, your going to be doing something called Bodyweight excercise's. Here's the wikipedia list:
Crunch
Dip
Jumping Jack
Press up, or push up
Pull up, or chin up
Sit up
Squat
Pistol, or one-legged squat
Handstand Pushup
Lying Hip Swing
Burpees
Mountain Climbers
Grasshoppers
Side Bends
Squat Thrusts
Plyometric Pushups
Box Jumps
Pike Press
One Arm Pushups
Russian Twist
One Arm Chinup
Diamond Pushups
Hindu Pushups
Planche Pushups
Front Levers
Plyometrics and other things like that are good too (but are generally very hard unless you have some athleticism and some strength and endurance)
With a little innovation, you can also work your forearms very well. Get ahold of a wooden dowel and drill a hole (width wise) throught the center. Shorten it till its a little longer then shoulder width. Now run a thick string through the hole and knot it. On the other end, tie anything weighing around 3lbs (trust me, youll want to start at this weight) to it. Now hold the dowel in your hands and roll it, raising the weight up gradually as the string wraps. Now do the same going down and then up, using the opposite motion. A good goal is to get 3 up/down's before it burns to much to continue (WARNING: It burns a LOT 
)
Really, you just have to be a little resourceful to get a workout in if you can't buy.
NOW, if you do get dumbells, then you can do all kinds of things. Really just check any workout site.
Theres: Dumbell curls, Tricep extensions, Skull crushers, Sprinter squat, Back rows, shoulder shrugs, Arm raises, Dumbell Fly's, Shoulder press, etc, etc.
Really, the best thing to do would be to get some dumbells and do a little of both sections, but if you absolutely must, bodyweight excercises can suffice.
Though your not really going to gain much muscle mass, rather, you'll lose fat and build strength and endurance. It takes heavy weights to just gain pure mass. Generally the rule is (in any one set): 2-5 reps (pure Strength, little mass), 6-10 reps (maximum mass, with some strength), 12-15 reps (pure endurance, little mass).
I've been doing about 3 sets of 5 reps each (pure strenght, little mass) and I'm very pleased. So far the most significant gains I've gotten since I started 3-4 months back was increasing my leg press rep weight (not 1 rep max) from 290 to a whopping 470. And I haven't gained a pound! Still 170, though that can be attributed to some fat loss (not much, I'm skinny by any standard, and most gains was probably nerve type) and such (lots of noticible toning, but not much mass gain aka. waterweight, needless pounds , yay) The important thing is repitition and to work at it. Good luck!
Edit: Just read some other posts, Yes, your diet is extremely important. Read up on catabolic and anabolic states (before, after workouts) and that stuff to get a little understanding. Carbs, fats (the good kind) and protein in sufficient amounts is extremely important.
