When you return from your mission, MyLDSMail will display a message about how to move your emails into a personal account upon logging in (if you want more information about this, there is an LDS Tech Forum discussion about it. Click here to read it; it's not very long). It will use Gmail's POP (Post-office Protocol) feature. It's a useful feature because it goes through your sent box, in addition to transferring things from your inbox. However, you cannot enable the POP feature while you are a missionary - it is only enabled upon your release. If you want to save your mission emails as they come in, in addition to using the POP feature at the end of your mission, here are some instructions.
Your MyLDSMail account should open shortly after you receive your mission call, or a few weeks before you leave to serve. I suggest setting this up sometime before you start your mission.
1) Log in to MyLDSMail.net. As shown, you log in with your LDS Account.
2) Follow these instructions from Google: https://support.google.com/mail/answer/10957?hl=en
The automatic forwarding setting may turn itself off in MyLDSMail after you set it up. Test it out by sending emails to your account and checking if they arrive to the forwarding address. If the forwarding isn't working:
1) Log in to MyLDSMail.
2) Go to the gear icon.
3) Click "Forwarding and POP/IMAP."
4) Under "Forwarding," "Disable Forwarding" might be selected (despite that you set it up to forward). If so, click "Forward a copy of incoming mail to..." and select your preferred options.
5) Test again!
That's about it! If you want to receive everything from your sent box as well while serving, you could add yourself to the emails you send (I'm sure there's another way to do it, if you search). You might also consider making a folder in a personal email account for your mission emails. I feel like I received a good amount of emails on my mission, and my inbox was only 5% full at the end, so don't worry about running out of space.
Also, don't forget to leave a copy of your passwords and important information (email, Facebook, credit card, etc) with someone!