how to get my apple computer to let me log into it remotely

You need to tell us what Mac with all its details + OS X version + how connected to the net. - ÇÇÇ

First, you should be asking this question is the Mac OS X forum associated with the version of Mac OS X you are running (Leopard, Snow Leopard, Lion, Mountain Lion, Mavericks, Yosemite). If you tell use the version of Mac OS X you are using, we can ask the moderators to move this post to that forum.

Back-to-My-Mac is what you would use if both Macs are yours using the same Apple iCloud account.

<https://www.apple.com/support/icloud/back-to-my-mac/>

<Set up and use Back to My Mac - Apple Support>

If you are trying to connect to someone else's Mac (a family member, or friend), then you can use iChat (older versions of Mac OS X) or Messages to initiate Screen Sharing.

<Messages (Mavericks): Share your screen>

You could also use TeamViewer.com which is very good at connecting to a remote Mac (or Windows, as it is cross-platform) across the internet and navigating through home routers.

<http://TeamViewer.com>

The next level of complexity would involve opening ports in the destination home router. This is non-trivial, and hopefully one of the above 3 methods will do the job. PortForward.com has documents providing step-by-step guides on how to setup port forwarding for a huge list of routers

<http://portforward.com/>

Again, hopefully, you do not need this level of complexity. But if you do please let us know.