There are lots of different ways that you can prepare for a workout. Some are better than others, and what works best can certainly be specific to the individual, but there are a few points that are pretty universal when it comes to properly warming up.
First, get your body temperature up. This doesn’t need to be anything fancy, but make sure it consists of low impact movements that aren’t immediately challenging the range of motion in your joints. Especially if you’re at an early morning class and you’re fresh out of bed, or if you have been trapped in the confines of a chair all day, it’s extra important to get blood pumping through your body before you ask too much of it. Don’t overthink it – when you’re sweaty, you’re good.
If you feel specifically tight in one area, work on some light mobility and stretching. If you have a legitimate issue that you know you need to work on, you should be spending some time working on that at home. Pre-workout, just make sure you are able to get into the positions that the workout calls for without issue. Getting warm before mobility work will only help.
The next time you show up to class early, try and spend a couple of extra minutes on your warm-up and see how much better you feel by the time the workout begins.