I wouldn't consider 3/4 to be "non standard".

My advice would be to find recordings of pieces in 3/4 and count along to them.

The "oom-pah-pah" pattern is a very common way to arrange a 3/4 backing. I suppose the most direct example is "Oom-pah-pah" from the soundtrack to the musical "Oliver!" - so listen to that first. In the chorus, they actually sing "Oom-pah-pah". "Oom" is beat one; "pah-pah" is beats two and three. In the verses you can practice without that crutch.

Start by spotting the downbeats, the "oom". Most of the time they are pretty obvious - a bass instrument or a drum will be marking them. Call out the downbeats by saying "one".

Once you can do that, fill in beats two and three. Often these will be emphasised by a higher pitched instrument like strings or the higher strings of a guitar. Call out these by saying "two three". And you've got it!

There are plenty more examples in pop/rock. Try "Norwegian Wood" or "It's A Man's Man's Man's World", or any one of thousands of country ballads. In classical music, of course there are lots of waltzes, minuets, etc.

Of course, not every piece in 3/4 uses an "oom-pah-pah" arrangement but once you can count 3/4 against an oom-pah-pah backing, you should be comfortable enough with a three-beat bar to apply it to other pieces.

Once you can reliably count time on recorded music, it should be quite straightforward applying that to music you are playing yourself.