Pedal on exercise bike fell off, not going back on

Which side pedal came off? This answer might help, pedals don't both screw in the same way.

If not, can you attach a photo? If you don't know the names we can help figure it out for you.

Two things may have happened:

1. It may have just unscrewed itself. As @likeprogramming notes, the pedals screw in differently. The left pedal must be screwed in counter-clockwise ("left") while the right pedal screws in the normal clockwise ("right") way. It is easy to cross-thread the pedal by having them at a slight angle when screwing them in. I find it is helpful to rotate the pedal bolt in the "wrong" direction for one total revolution before then reversing it and screwing it in, this helps prevent a cross-thread.

However, your description of the pedals only screwing in a few threads bothers me. If it's not because you're trying to screw the left pedal in the wrong direction and if it's not because you're cross-threading then ...

2. there's a chance that the crankarm threads were worn or damaged -- and that is why the pedal came out. In that case, you will need to drill-and-tap a helicoil into the crankarm. This isn't something a normal DIY person can do, but it is relatively easy for a bike-shop and should only cost around US$20-40.

Here's a labelled diagram for the crank part names:

If you are talking about the threads on the pedal there are three (or more possibilities)

1. It is cross threaded
   But if only one pedal come off then that is not the case
2. Not cross threaded and everything is fine
   But you are just not lining it up correctly
   It can be hard to get even good threads to align some times
3. Threads are damaged
   If it worked its way out then when it was barely in there was a lot of stress

Clean both pedal and crank threads with solvent and brush
If you don't have a parts cleaner type solvent then just a de-greaser or even dish washing soap
Put a dab of grease on the pedal threads
If you don't have grease then just stop and get some

Come in from the back side. If just the first few thread are messed up then coming in the back side should work. If you get several easy turns in before it sticks then most likely just some messed up threads on the front side. You typically don't want to force but if you have several turns in then you can force with a wrench to clean out the threads. If the works then try coming in the font side. If this does not work then take it to a shop.