First you'll need to buy an Apple AirPort Express. You can get them at the usual consumer electronic stores like the Apple store or Best Buy ...or pretty much anywhere online.
Plug-in the AirPort Express in between your current AirPort base station and where you want your Wi-Fi signal to be stronger. The light on the front will be yellow.
On your Mac - open the AirPort utility app located in your Applications --> Utilities folder.
When you open your AirPort Utility it should look something like this
In the top left-hand corner you should see a drop-down menu for "Other Wi-Fi Devices". Click on that -- the AirPort Express you just plugged in should appear.
By default the AirPort Utility will setup your AirPort Express to extend your current network.
See, it was that easy. Setup complete
Your wireless network on your AirPort Utility should now look like this.
The light on your AirPort Express should be green.
Now go try it out! Your Wi-Fi signal should be much better on your existing network.