OK, first of all you can't do it if you've been here too long already (think the cutoff is two years. edit: no, it's one year, see below) Assuming that's not the case:

• Have the eye exam first (any optometrist in your canton can do it, and will probably have the form on hand already. Saves you a trip.)
• Get a passport photo (e.g. from one of the instant machines you find in train stations.)
• Go to the cantonal driver's license bureau. (Yours is apparently in Füllinsdorf.) Tell them what you want to do, fill out the forms they give you, hand them back.

That's it. You will get your license in the mail in a few days, along with a bill for CHF100.

Oh, be sure and tell them you need to keep the US license, otherwise they will dispose of it for you.

EDIT: If your US license has been recently renewed (i.e. since you've been resident in Switzerland), you might run into trouble. They want proof that you had a valid US driver's license as of the date you moved here. If you still have your old US licence kicking around, take that - otherwise you will have to order the records from your home state.

edit: no, it's one year. You can keep driving for up to 2 years on a foreign license, but if you want to exchange the foreign license for a Swiss one, that has to be done within one year.