It helps to do this with a partner who serves as a Catcher for when you get the window loose enough from the caulking to remove it out of the shell.
Remove any excess caulk around the outside.
On the interior remove the screws that are in the interior trim ring.
On the outside take a thin, flexible putty knife to slide between the window trim and the shell going all the way around the perimeter so break that bond of the caulking under the aluminum trim. I have also used one of the little bent O ring removal picks to dig out stubborn caulk if the window does not push out easily. You can find the little O ring picks at any hardware or auto parts store, they are not expensive.
Set the window down on an old towel on top of a table or other horizontal surface and clean all the old caulking off of it. If your window needs new rubber seals and track run felt for the sliding now is the time to replace those items and get it in good operating condition.
Then clean the surface of the fiberglass.
Next you will apply butyl rubber tape against the aluminum flange or against the fiberlass and set the window back in place. Be sure you get it centered so that the flange does not have any gaps from the opening too close to the edge of the exterior trims. Push the window firmly into the butyl tape. Then the person inside begins to install the screws. When secure it you don't want to start from one end and work towards the other, instead do the following. Do the corners first working on the diagonal mate. Then the center screws top and bottom. Just keep on working on the opposite pairs of screws.
Don't be in a hurry to remove the excess butyl rubber tape that squeezes out on the exterior because it will continue to creep out over the next week or so. No point in trimming it after the window is put in and then be frustrated that you have to trim it again several more days in a row.
Other tips to make the job eaiser:
keep the rolls of butyl rubber tape in a gallon sized ziplock bag in the refrigeration. The warmer the weather the stickier it gets and when it is sticky it is a lot more difficult to apply it. But it will be nice and firm and not too sticky when it comes out of the fridge
. That will make the job go a whole lot easier and faster than trying to deal with it sticking to your fingers.
Also it is easier to cut the butyl tape to length with a pair of scissors than it is to try to cut it with a knife.