First, we have to assign a static IP address to the Raspberry Pi on your home router. Most home routers will allow you to do this. Read your home router manual to learn how to do this.
Now you can access the Raspberry Pi remotely via SSH ssh <username>@<ip-address>
For example, if you gave 192.168.1.123
to your Pi, then you can connect to your machine like so
ssh pi@192.168.1.123
The default username is pi
and the default password is raspberry
. For security reasons, you should change your password.