For each of these progressions, I will be giving a progression level, once you get to this progression level, you are strong enough to move onto the next exercise. If you are having trouble increasing your repetitions have a look at this blog post for a simple way to increase your reps on an exercise.
Step 1 - High recline row.
Find something you can throw around a surface, rings are preferable, but you can use anything that can hold your weight will work, I am using a karate belt here. Stand with your feet directly underneath the anchor point with your feet shoulder width apart. Lean back, (bottom left) and pull your arms in until you are standing upright (bottom right). Lower down to the starting position and repeat.
Progression level: 3 sets of 25
Step 2 - Recline row.
Over time, slowly move your feet further forward (6 inches at a time works well, work up to 3 sets of 25 each time). Continue moving your feet forward until your shoulders are directly under the anchor point, row up until your hands are as close to your chest as your flexibility allows you to, lower down and repeat. At first, reach the progression level with your legs bent at 90 degrees, then straighten your legs out and work up to the progression level again.
Progression level: 3 sets of 25
Step 3 - Chin up hold
Jump up so that your chin is over the bar, and hold it.
Progression level: 3 sets of 20 seconds
Step 4 - Half pull up
Jump up so that your chin is over the bar, lower yourself down until your arms are at 90 degrees, come back up until your chin is still over the bar, repeat. If you cannot go down to half way, only go quarter way down, reach the progression level, then go to half pull ups.
Progression level: 3 sets of 10
Step 5 - full pull up
Hang from the bar, so that your arms are slightly bent, pull up until your chin is over the bar, lower down to the beginning position, repeat.
Target level: 1 set of 20
Hope this article helps
Enjoy the gains
Alex