Fez,
DoD [i]can be[/i] a free game you download off the Internet. That is how it started out. Like it's more popular brother, Counter Strike, DoD (Day of Defeat) is a modification (mod) of the best-selling game Half Life.
While Counter Strike is a squad-based counterterrorism-themed game, DoD is a somewhat-squad-based WWII-themed game.
As mentioned above, it's "mostly" available as a mod of Half Life. When you purchase and install Half Life, you can then download and install DoD for free.
[i]Alternatively[/i], and only recently, DoD (and Counter Strike both) has been offered as a "stand-alone" game. IOW, you wouldn't have to have Half Life if you purchased a stand-alone copy of DoD (referred to as "DoD Retail").
However, the "best" way to do it - in my own opinion - would be to purchase and install Half Life (I'm sure you can find it for next to nothing - I got mine for $15 last year). Then, go onto the Internet (to somewhere like [url]www.fileplanet.com[/url] and download a program called "Steam". Also download Day of Defeat. To a point, version doesn't matter.
When you install this, it will "take over" Half Life and any other Half Life based games in there. They will thereafter be located in your Steam folder. When you want to run HL or any HL-based game, you will need to run Steam first. When it is starting, it checks for its own updates. Then from the Steam menu, you will select the appropriate game, which will update itself before you can play.
Best of luck and read some of these other threads in here to answer a lot of your subsequent questions.