Many good comments. Just to add to it. Because a slow topspin serve can look like a backspin serve if you don't know what to look for, and vice versa, here are a few things.
I am talking about flight and arc of the ball on a serve. But I personally think you need to look at both the body position, what the racket does, the contact, where on the bat the ball contacts, position of the elbow. You have to look at those and the path, arc, of the ball.
Der_Echte made a good point about how a ball that has a first bounce closer to the end line will probably be long and one close to the net will probably be short.
A short topspin ball, even if you don't full see the kick, and it looks like it is floating, will have a rounder arc in its path. An underspin ball will have a flatter arc.
I think sidespin are a little easier to see because you just see the curve (left or right) and how much curve. A lower flatter arc will show underspin and a rounder arc will show topspin.
So, to disguise underspin a good player will have the ball come up a little off the racket to drop for the spin. Which almost duplicates the rounder arc from a topspin ball. But it still looks different.
A friend who is a pretty high level player (2600+ USATT) told me he just can see the spin spin when he looks at the ball. I try. I watch. Sometimes I can see that a ball is loaded. Sometimes I can see that it is top or underspin and I just see it. But not most of the time. So you just keep working on it.
Another friend who is not quite as high a level told me that topspin will leave ahead of the racket and backspin will lag behind the racket. I don't know if that is always true but that is a cool one that helps me quite often.
So keep watching all the cues from the server, and keep watching the arc and path of the ball. And keep trying to watch the ball to see if you can gauge the spin.
I sometimes have trouble seeing dead balls and then sometimes I go, "Oh, wow, I can see it has nothing!"