You're fertilizing and aerating the cultures too? You started with live algae? You've got them in front of a bright light source?
If you can see the tint of the water, just getting a drop of it onto a slide should be enough. If you've got coverslips, they are the best choice, you put one on the drop to squish it down and then things are easier to find. Basically, a microscope, moreso at high magnification, has a very shallow depth of focus, so even with a 5x objective, for example, you can't keep the full depth of a normal droplet in focus.
So presuming 10x eyepiece(s) and a set of objectives, phyto will look very small but maybe noticeable at 5x, a little better at 10x, and closer to the shape of an object you can identify at 20x. Beyond 20x, don't bother unless you have the cover slip, or even the water currents in the droplet will push anything in focus out of focus in pretty short order. You should get the surface of the slide/edge of cover slip in focus (so you know it's close to the right height), then scan in and out slightly to see if other things come into or out of focus. A small opaque object will look like a blurry round smudge when out of focus, so if you see smudges drifting around like they are in water, try to focus them. Try increasing or decreasing the light through the sample, too, the right lighting will dramatically improve contrast.
To mount the slide, take a clean, flat slide and put a drop of culture on it. Then drop a cover slip on it (one edge on the slide, then sort of hinge down to reduce the number of bubbles). Then take a bit of paper towel or tissue and blot on the edge of the cover slip - this will suck some of the water out from under it and make the distance between the coverslip and the slide narrower, which should make it easier to keep the sample in focus.
I probably wouldn't bother with the 100x objective at all - it's likely oil immersion and needs a drop of the right oil on the coverslip to couple the light in, and especially with an inexpensive microscope, probably won't be a high enough numerical aperture to give you a much sharper or contrastier image than your second highest magnification (though it would be larger in the eyepiece.) If you have 15x or 25x eyepieces, I would swap them for 10x if available or just stick to lower magnifications mostly.
In terms of culture density - I just go by opacity. You can get a Secchi stick to measure more specifically the density (with no microscope), but you will develop a sense of what "looks good" in your vessels of choice and anything more transparent isn't done or is having trouble. Use the microscope for identification/troubleshooting/curiosity - while you can absolutely do a cell count to get a better approximation of density, it's tedious and unnecessary work for a hobbyist culture.
