How do I know if them gem(s) in my piece are glass or spinel?

Aside from a presidium tester, there are several easy ways to identify which is which -

Jewelry items that have multiple small gems are going to be rhinestones. Rhinestones are made of glass. Spinel jewelry almost always has just one larger gem.
This one is really important - green spinels are a very warm lime green color, and uranium glass is a cool tone peridot color.
Spinels are always found in gold and sterling silver. Spinels will not be found in costume metal jewelry. Costume metal jewelry will have glass. However, uranium glass can be found in gold and silver also. If you have a gold/silver piece and aren't sure, you can take it to any jeweler who can test it for you. Just make sure they actually use a presidium and not just their eyeballs because it's easy to get it wrong, and most jewelers do not know what spinel is. A presidium can at least identify it as glass vs. gemstone. I'm also always happy to answer identifying questions! I can usually tell with good pics.
Spinels tend to be much larger gems with a lot more and fancier faceting. This isn't always the case but it can be a clue. I personally have never seen a spinel smaller than 6mm, and even that is very small for a spinel.

Spinel gemstone in an unprotected mount

If the gem is in an unprotected setting, meaning the edges of the gem stand out where they can be knocked, unprotected by the mount, then it's more likely spinel. This is not a hard and fast rule but just another clue.
Because spinels are hard stones, they don't get chipped and scratched as easily. If the gem has a lot of wear or damage, it's more likely glass. This is not a hard rule as spinels can still have wear over a hundred years, but one of the clues you can look at.

Synthetic spinels have been made since the late 1800s, but started being manufactured in larger quantities during the 1920s. Not a lot of sellers know what a spinel is, and they are very often misidentified as other gemstones. They are also sometimes mislabeled as uranium glass, however, word about them has spread quickly (thanks to yours truly 😁) and it appears this is happening less as the years go by.

I always recommend spinels for engagement/wedding rings for uranium collectors, and anyone that wants a uranium glass ring for daily wear, due to their durability. They glow just as bright and as green as uranium glass under both 365nm and 395nm.