So it is important to note that while completely static points do exist in 1:1 scale, they are exceedingly rare and as far as I know not used on any currently operating electric tramway.
The vast majority of points on modern systems use a pair of moving blades just the same as heavy rail points. As you point out they are indeed a maintenance item and the flangeways and slots in the road the point blades move in do have to be kept clear of debris. The reason why you usually can't see any point lever or similar by the side of the road is that the point mechanism (either manual or power operated) is completely under the road surface.
If the points are manually operated, they're changed by a "points bar", basically a short crowbar you stick in a slot between the rails, and in the flangeway to lever the points across. A spring or weight holds the points in position one way or the other.
Here in Melbourne a tramway staff member changes a set of points with the points bar. As you can see this is an infrequently used set of points, so they have had to use the points bar to scrape some dirt out of the flangeway to allow the blades to move.
Like mentioned above points can have either one or two blades. Single bladed points were very common on old systems because of their simplicity, but modern systems almost exclusively use double bladed designs like in heavy rail. Part of the reason for this is that for a single bladed set of points the wheels have to roll over an extra gap in the rail, with resulting extra noise and vibration.
Here is a single bladed set of points still remaining on the Melbourne tram network, though they are becoming rare now. The moving blade is on the right (set for the diverging direction) and the static part is on the left. The metal plates in the roadway cover the spring mechanism that holds the blade over. The spring also allows the blade to spring back if pushed aside by a tram in the trailing direction, which is how the vast majority of points work in places where the tram always takes the same route in the facing direction.
The advantages of single bladed points also apply in modelling, here is a representative example on my tramway.
The blade is on the left, set for the diverging direction. Only needing to clean out one blade is a big advantage for running outside.