OK that picture helps everything - that isn't big by any stretch of the imagination, and it certainly achievable with bodyweight work.
The think about that physique is the low body fat and moderate muscle mass. To achieve the first part focus on your diet, assuming you are just lacking in size, eat close to maintenance or a little over.
With regards to how to build muscle, as people have stated, the key is volume. Focus on being able to do exercises in the 10-15 rep range with good form for 5+ sets. The challenge with body weight exercises is increasing difficultly. Unlike with weights were you can just increase the weight, your challenge is to decrease leverage.
Chest exercises can be increased in difficultly like so:
- Push-ups on the knees
- Standard push-ups
- Wide-grip push-ups (A narrow grip works the triceps more)
- Incline push-ups (the greater the incline the more the deltoids are worked)
After a certain point push-ups may become easy, but you can just throw on a backpack with some weight - books, sand, small children - to increase the difficulty.
Back exercises include:
- Body weight rows (A broom across some chairs will work)
- Incline body weight rows (Elevate your feet on a box)
- Chin ups (Supine grip)
- Pull ups (Pronated grip)
Again, a backpack can be helpful. But by the time you can go 10+ reps for 5 sets your lats will look awesome. Regardless of what people suggest, you can get a great back with body weight alone. Will you win Mr. Olympia - no, will you impress most people - yes.
Even just devoting a day to pushups and a day to pull ups will work your shoulders quite well. Your front deltoids, which are "meatier" and help build that shoulder contour actually play a large roll and are worked thoroughly in Transverse Flexion or pressing while your posterior deltoids will be worked by the rows and pullups. While both pushes and pulls will work your lateral deltoids. Both exercises have the added benefit of working your core for stabilisation - i.e. your abs, obliques and lower back - as well as the oft neglected serratus anterior - those muscles that kind of look like ribs or fingers but only show on boxers and posers.
Day A: 10-15+ reps x 5 sets pushups
Start on the knees and move to the next exercise in the list once you can hit 20 reps on your last set.
Day B: 10-15+ reps x 5 sets pullup variation
Start with rows, and move through the progressions as above.
Day C: Rest.
Repeat A-B-C until you look awesome. As I mentioned, this kind of work won't have you winning Mr. Olympia - but if you can do 50+ pushups or pullups in a single session, you will have a strong and enviable physique like the picture you posted.