you can plug an airport express into any power outlet in the house, and it can extend your network. (it only needs to be connected to power, no ethernet)
i would place it somewhere near the mid point of your house, if it's too far from the main base, it can't get a good signal to repeat.
you do sacrifice some speed when you do this, but for internet browsing, you probably won't notice any difference. Traffic all on your network (like time machine backups, or moving files from one computer to another) will be slowed down.
the speed drop is caused because the middle man has to spend half of it's time talking to the main base, and half of it's time talking to the remote computer.
to do the initial set-up, i would run an ethernet cable from your laptop to the express. you can locate the express somewhere that makes it easy to do this, and then once it works, move it to the final location.
*you can set up over wireless, but it's easier to recover from issues if you are wired.
** another option is wireless ethernet from extreme to the express, and the wireless from your laptop to the extreme.
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if speed is an issue, and you can run a ethernet cable to where you want to put the express (
powerline networking is a viable option here) there are other ways to accomplish the same thing, that are a little more robust.