Hi, welcome to the forum and congrats on the new phone
(sorry took to long to write so others beat me to it)
I'll try to give you a start on this, feel free to ask if this doesn't help.
It's easy.
But you need to understand that there are free apps and paid apps.
Depending on what country you're in you won't get access to the paid apps (unless you get hold of a sim from a country with access to the android market).
So... the first option, using the app on your phone called Market.
First, enable wifi so the phone can get online.
If you don't have a wifi network you must use 3g data traffic, mind you, this cost extra so see your phone company's pricelist for data traffic.
Then just start the Market app on the phone and with it you can browse/search the andriod market and install the apps you want.
Tip: From within the Market app you also get updates, just hit the Download tab to see installed apps you've downloaded from the Market. From there you can also uninstall them.
Second option,
Still using the wifi (or 3g data, just remember that using 3g cost extra) open the app on the phone called NeoReader.
Browse the Internet with your computer (search google for free android apps) and some of the pages gives you an 2D QR barcodes. Simply point your camera on the phone on the bardoce and it will ask you if it's ok to visit the address - click yes/ok and you'll start download and install the app.
See examples of such barcodes here :
(the barcode is the square black'n white stuff on the right)
ADW.Launcher for Android
Third options is to visit pages where you can download the app you want.
This comes in .apk files. Just connect your phone to the computer with the usb cable (no need for either wifi or 3g data on this one).
Copy the .apk file to the SD card on your phone.
To install it, you'll need an app called AppInstaller (get it from Market), and from that app you'll install the .apk you downloaded.
Hope this helps