It's a question get all the time: "Is my phone rooted? How can I tell?" Maybe you picked up your new Android phone second-hand (it's a great way to save some cash, and there are a lot of great used Android phones out there!), or the cryptic directions for rooting your particular phone seemed to forget an easy way to check if it was successful, or maybe your crazy brother was messing with it while you were in the shower.
No matter the reason, checking if your rooted is easy as pie, and is a quick introduction to a tool you might very well be using now that you've switched to the dark side and rooted your phone.
Open the Android Market and search for a terminal client. There's several free ones, and they all work great. If I was forced to recommend one, I would choose Connectbot, but any of them will work.
Open the terminal app, read through the instructions (if any) you see, and you'll be faced with a text entry prompt. If your prompt is the pound sign ( # ) -- you're rooted. If you see a dollar sign ( $ ), try entering the command "su" (without the quote marks). You might see a dialog asking for permission from the SuperUser app, which you can safely grant. If the prompt changes to the pound sign, you're rooted.
Remember, root is the boss. You can do anything while you're root, including many things that can "break" the OS and cause all sorts of trouble. Read all the guides and warnings before you try anything, and by all means ask questions in the Android Central forums!