First, if you haven't done so already, get the MMNET.zip file here: http://www.mekwars.org/MMNET.zip. Once you've downloaded and saved it to your computer, unzip the files.
You will now have a folder called MegaMekNET. Inside this folder, run (double-click) the MegaMekNET.bat file (I also suggest creating a shortcut to this file and placing it on your desktop or with your other game shortcuts) to launch MMNet for the first time. You will see this:
Choose a user name (fields are case-sensitive). Leave the password field empty at this time. Do not change the IP Address or ports. You should then see this pop-up:
Click the Yes button to continue. The client will begin downloading updates. Once it has finished updating, the Login screen will appear. Login with the same user name you set earlier. You will see this:
Click on the Maximize button to expand the window. You will see two links in the Main Chat window.
Click the "Click here to get started" link. The following message will appear:
Now click on the "register" link. A new pop-up window will appear:
Fill out the form, use the same password for both password fields (remember, these fields are case-sensitive). Use a valid email address that you actually check. THIS IS IMPORTANT!!! A validation code will be sent to that email.
Now you are ready to get started. More information is here: Getting started