Being able to navigate without GPS is a skill you should definitely learn because it can come in handy from time to time, and real world navigation still relies a lot on the old methods.
Buy yourself a decent compass, one that has a nice big transparent baseplate with scales for distances and a good dial. Silva compasses are excellent tools and fairly priced, but I don't know if they're available in your part of the world since Silva is a Swedish company.
Then get yourself a map of your area. A 1:25'000 map is ideal for finer navigation and for learning, whereas a 1:50'000 is going to cover a larger area while still being suitable for fairly precise navigation.
That's really all you need to get started. You could throw in an altimeter too, but that's not really necessary, especially if you live in a relatively flat area.
Now you need to learn how to set and read the map, plot your position, take a bearing, count paces.
I could explain all of this, but I think it's going to be a lot more simple -and enjoyable- for you if you take a look at Glenmore Lodge's navigation and orienteering videos on YouTube. Glenmore Lodge is an outdoors centre in Scotland and they made the best videos on the topic.