This will be long. So get comfortable. Now first I have to say, I am only okay at this memeing thing. You see my stuff. But what I do to get what I feel are my BEST ideas is avoid the very common. Like If I am going to use a common template I like to make the caption really good. I like to do mash ups of templates too. If you don't have a lap top I don't know how easy editing is. Some people do it from their phone, some do not. It's a preference.
Anyhoo, I take pics of things I see out in the world. Something funny that will make a good original meme. Like that Lite Beer meme I did. I spotted that balloon at the grocery store a few years back. I have used it a couple of times and both times the meme did pretty well.
I like to jot down ideas. In my day things happen that are annoying to the general population, or funny, or whatever. I make a note and later try to get some interesting template for it. Sometimes one of the popular templates if perfect for sharing a relatable idea. This also keeps me in supply with ideas when I run low on inspiration.
Try to take impossible things and create a visual. The Eye Scream for one. When you say "Ice cream" it sounds like "Eye Scream". So I searched images until I found what would be good to edit in to a template. Just general creativity. Puns are always good around here. Taking human types of scenarios and applying it to animals is always good. Stuff like that. It takes practice too. No one is great from the beginning. The more you reach for good ideas the better you get.
When you browse memes you may get an idea off of a meme you saw. Use that. When searching google for images you may spot a funny image and get a good idea from it, use that. This is just how I operate.