Quick overview of how to capture microscope images of histology plate or fluorescent plate
For fluorescent microscopy images, wondering if I actually need a fluorescent microscope, or if I can make do with a regular optical microscope.


You need a fluorescence microscope. You need to be able to excite your sample with a narrow wavelength of light, and then image a different wavelength of light that is emitted. You need mirrors, emission and excitation light filters for that. You also need to understand the process. If you don't, having software to do the 'thinking for you' such as overlaying the different color channels is a nice thing, but then it's another requirement.


  If I need a fluorescent one, wondering if there is anything else needed, like special lighting or special materials for tagging the cells, which seems like it might require extra stuff like centrifuge and who knows what else.


Samples can sometimes have autofluorescence (e.g. the chitin that makes up the cuticle of insects is autofluorescent) but most samples are not. Almost always a fluorophore is used to stain the specimen for something. These can be cheap or very expensive, depending on what you want to stain. This really depends on your sample and how it is prepared. And know that most 'good' samples' are dehydrated or are treated by chemical fixation, which requires chemicals you cannot usually find at a local pharmacy. It depends on how ambitious you want to get as an amateur microscopist!

Also, you won't need a centrifuge.


  For the histology slides, wondering generally what it takes to do that too, if I can get by with a regular microscope.


You can get by with a regular upright widefield microscope for sure. If you perform the sectioning well (making thin slices of your sample) then even basic microscopes will produce fascinating images, provided your lighting is good. It helps to have a condenser or a nice lamp and some thin and clean glass slides for well illuminated images.


  Maybe fluorescent microscopy requires advanced biotechnology of some
  sort, which is sort of what I'm wondering, what the basics are.


It requires a little bit more optical work. I would stay away from it unless you are serious, because it takes quite a bit more work and equipment to make it minimally workable. Normal microscopy is certainly a lifetime of fun if you have the desire to find interesting samples and work to make them good for imaging.

Addendum: the principle of fluorescence microscopy is quite simple but aligning everything is actually quite difficult if you are an amateur with no specialized tools. Here is the principle only, notice how the input and output must be aligned and the small objective lens has to transmit both excitation and reflected light:



And here is an example of a basic lab stain for two elements of the cytoskeleton (actin in red and microtubules in green) and a DAPI-type stain for nucleic acids (that shows you the DNA-rich nucleus in blue). The crispness of the image really depends on the use of at least two or three lasers (not epifluorescent illumination, i.e. "lamp nearby") to produce the necessary and specific narrow excitation to separately image the different channels. The light detectors are in black and white (for increased resolution), and only in post-processing are they color-coded to make the image pretty. 



For a start I would begin with the basics! Pollen, cells on the inside of your cheek, blood, a single onion layer (...is a monolayer of cells, perfect for imaging), anything else you find and can think of! And find yourself a nice stain, or a nice dye or ink that is partially permeable. The world is your proverbial oyster at this point.