Here's a machine that is so simple, with such a charming design, that it will take you less than one evening to it apart, clean it, and put it back together again.
FYI: the machine on the left is an American 1. The one featured on the rest of this page is an American 2. The difference is in the size of the index. And don't you ever forget it!
The ad tells us the American was sold in its days for 5 dollars. The value of this marvel has kept up with inflation to say the least...

This is the American as it came from the attick (or wherever). The central pointer (the swinging sector) is used to select the letter. The button on the left (barely visible to the top left of the index) is pressed to print a letter. The button at the front produces a space.

Although the carriage moves freely, the two buttons do not move it forward. Something is stuck.

1. Remove these three screws to take off the carriage and the index plate.

2. Lift the carriage, the index and the swinging sector that held the rubber type. (On most americans the rubber type is gone.)

3. Remove the bell and next the two split pins (1 and number 2 that is under the machine) to release the two button bars. Mind the spring on bar 1.
Number 2 will come off after you've released the spring (3) by pushing it forward and pulling it up.
Here it turns out the machine is stuck because there is rust on the alignment pin (4).

This is where the serious and careful cleaning start. Instruments: water, soap, and polish.

Halfway there...

When everything is clean and shining, reassembly starts with the spacing system. Note the nice brass spring that showed up fom under the dirt.

The American in pieces.

Here's what heavy polishing will do to the swinging sector. It is made of beautiful shiny brass:

Here's another one for the mantelpiece.