sure.
start by creating a wallet at blockchain.info/wallet - this is a lightweight web-wallet that is easy to use, offers multi-factor authentication, tools to backup your wallet keys, etc. This'll save you mucking around having to install the bitcoin-qt client (the basic Bitcoin client) and downloading the entire blockchain which can take several to many hours.
generate a receive address in your blockchain.info wallet. Label it "pool mining receipts" or something like that.
Download guiminer from wherever you get guiminer from (it's been a while so i don't remember, and i wouldn't post the link anyway, cuz people are paranoid about clicking links in the newb forum). it's fairly simple to install. You'll want to throw that sucker on the PC with the best video card. using the hardware mining comparison list linked earlier up the thread, you can see what cards average what for hashrate. Basically, if you ain't got something ATI/AMD on that list, it's really not even worth the effort. For example, with recent increases/changes in the network difficulty rate, my 6770 card, which generates about 180Mhash/sec. Mining in the Slush pool, I make about a bitnickel every 18-20 hours. Yep. 0.05000000BTC. so, that's about 1BTC every 360-400 hours, or every 15-17 days. So 2BTC a month, and I'm probably using far more than $40/month in electricity to do so (luckily, I don't pay for electricity here).
If you have a HMCL (hardware mining comparison list) compliant card, and still want to try it, pick a mining pool and have at it. I suggest Slush's Pool, as it's probably one of the simpler ones to sign up for and get started. You can tell if your mining software is working by looking at the default tab of guiminer. Down in the bottom right corner,you'll see a Mhash/s value. if you are actively mining, this will be a number that fluctuates slightly every second. (mine varies about 2Mhash every second)
And there ya go. there are lots of help threads to get you going if you have trouble configuring guiminer, etc. Once you're up to speed on how to mine, start reading threads on securing your hoard of bitcoins once you start to acquire some. I don't keep a lot of btc in my blockchain.info wallet, it's mainly just a clearing house. When I buy BTC, they get sent to me via that wallet, so that I can transfer them either to a investment site, or to an offline wallet. an offline wallet is basically a wallet executable on a memory stick, or even on a netbook or something that you only connect to the web when you need to access it, then you take it offline again. There are also paper wallets (where you print out your private keys and store them someplace securely), physical bitcoins (cascacius, i know i probably spelled that wrong) where the private key is hidden under a hologram sticker, printed bitcoin bills, etc. Plenty of ways to store your bitcoins securely.
Once you get into the social aspect of bitcoins, i just have one piece of advice. STAY ALERT, TRUST NO ONE. Distrust everything. Or at least, don't automatically trust anything. There are several mechanisms to gain rep/credibility, the OTC (i haven't figured that out yet, it's an IRC channel, i think), be active on the forums here, don't beg or try to borrow, etc. If you are going to buy bitcoins, use a reputable exchange service, ie nothing involving paypal, and if you are using bitcoins to buy goods, use an escrow service/person. Escrow is when a community-trusted 3rd party agrees to be a holding point for the bitcoins in a transaction. Party A wants to buy a widget from Party B. They agree on a price and an escrow provider. Party A sends the funds to the escrow provider, who confirms receipt of the funds with both Parties. Then Party B ships the widget. When Party A receives the widget, they inform the escrow provider, who transfers the bitcoins to PartyB. Most escrow services will charge a small fee to hold the funds. Some don't, and will do it for the good of the community.
Bottom line is, BTC is just like real world stuff. If a product or service sounds too good to be true, it likely is. There are a lot of scammers out there. Be friendly and open, but be cautious about where you send your money or bitcoins. There are some scams which are so obvious they are like the equivalent of some homeless-looking dude walking up to you on the street and asking you for $1000 so he can start a street-corner hobo dance academy.