Hi, and a warm welcome to the game!
First of all, I'd recommend you make sure that you have the latest version of the game. To check this go to the main menu and at the bottom, I think it's the right hand corner it will say Version X X X Build X X X X. If it says anything below 1.4.2 go here (http://www.shipsim.com/downloads/patches.php) and download the 1.3 > 1.4.2 file. Double click on it once downloaded to install.
Once you've done that, in custom missions you should see a huge amount of missions, click on one of them and it will say "Download Mission" on the right. CLick on it, and you'r ready to go.
Hope this helps!
Mike