I made a portal with the Twilight forest mod, but it just appears to be a normal portal, and when I jumped in it doesn't teleport me at all. I tried making the portal again but the same thing happened. I made sure I had no incompatible mods.

Sounds like #253 which will be fixed in the next update. For now, make sure your portal frame only has vanilla grass blocks.

Okay si I managed to get the portals "working. Apparently when I jump into it I get teleported underground or on the surface, where I somehow suffocate. I also get stuck because the rest of the area won't render.

You'll have to give more info that that. If I jump into a TF portal, I'll neither suffocate (disregarding #248) nor are there any rendering issues. I generally always recommend reading this article to anyone who hasn't yet.

Okay here's a more concise explanation. So I get the portals somewhat working, and when I first jumped in I was stuck inside a cave and couldn't move, so I had to go into spectator mode to get out. Then I realized my world was a weird amalgamation of the overworld and twilight forest. I then changed to survival and suffocated to death while I was outside. Then I respawned n the twilight forest with no portal, so I had to use journey map to escape. I then tried it again in a different are, where I got stuck in mid air, while half of the area didn't render.

That's better but it doesn't explain how to reproduce it.
Please at least have a read through the "Show me how to show myself." and "Works for me. So what goes wrong?" sections. Best if you read it all though.

Actually, it seems to have fixed itself.