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.

There are plenty of 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.

Start by spotting the downbeats. 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!

This "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 if you're still having trouble. "Oom" is beat one; "pah-pah" is beats two and three.

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