Choose the download location C:GamesDoom3darkmod or ~/.doom3/darkmod in Linux.
After download, make sure you don't have duplicated the folders, like C:GamesDoom3darkmoddarkmod or something.
You'll find an executable tdmlauncher.exe in your darkmod folder, i.e. C:GamesDoom3darkmodtdmlauncher.exe. Use this to start The Dark Mod.
To update TDM to receive future updates, just run the tdm_update.exe application found within the darkmod folder.