This Instructable will show you how to assemble your Iron Gym ($29 ish).
Having put one together myself, I will detail a certain flaw I encountered during my personal experience, and how to overcome it with ease.

This piece of equipment is great because the user does not have to drill any holes in their door frames. It functions off of grip and pressure due to the user's weight pulling on it.
Note that the Iron Gym is designed for individuals weighing 300 lbs or fewer.

There are five main pieces, six screws, six washers, and four nuts. You also get an allen wrench and a hex wrench.

Step 1: Attach Arm Bars to Grip Piece.

Start with the long plastic bar which has a pad of grip on one side, and two rounded slots on the other.

Use the medium size screws to attach the arm bars to the grip bar.
Insert the screw into the grip piece (fitting the squares in place) and through the arm bar.
Then add a washer followed by a nut on the end of these screws.
Secure tightly using the hex wrench.

Step 2: Attach Pull-up Bar to Arm Bars.

The pull-up bar is two pieces which slide together, one into the other.

Normally you would insert the small screws through washers and into the bars to connect them, but on my pull-up bar pieces, the holes did not line up correctly.

In case this happens to you, join the two pull-up bar pieces appropriately but don't insert the small screws to make these two pieces one, just yet.

With the pull-up bar "together," use the longest screws to attach the arm bars to the pull-up bar.

Step 3: Pull-up Bar Tweak.

It's important to have done it this way because if the pull-up bar holes were not lined up but you secured them with the small screws, the whole device would end up warped which is not at all safe.

With the pull-up bar combined but still loose, it is attached to the arm bars which are connected by the grip piece.

You should be able to tell if the holes in the two pull-up bar pieces are properly lined up.
If they are, use the small screws.
If not, you can do what I did using the allen wrench and tape.