A telescope at 50x sees about one degree of sky, which is why pointing one at anything without help is close to impossible. The finder is the accessory that solves that, and there are three kinds that solve it in different ways.
The optical finder
A small low power telescope, typically 6x30 or 9x50, bolted alongside the main tube with a crosshair in it. It shows a wide field with fainter stars than the naked eye, so you can star hop to a target and see it before the main instrument does. The larger sizes are genuinely useful instruments in their own right.
The red dot finder
A window projecting a red dot onto the sky with no magnification at all. You look through it with both eyes open and put the dot on your target. It is faster and more intuitive than an optical finder for bright objects and useless for anything the naked eye cannot see, which is why many observers fit both.
Aligning it, which takes two minutes and is always worth doing
Point the main telescope at a distant object in daylight, centre it in a medium power eyepiece, then adjust the finder's screws until its crosshair or dot sits on the same thing. Do this once in daylight rather than fumbling at night, and check it whenever the finder has been removed.
The one safety rule
A finder is a small telescope with no filter on it, at eye level. Before any solar session it must be capped or removed, and a red dot finder switched off, because the commonest solar accident is somebody putting an eye to an unfiltered finder out of habit.
Questions people ask about finderscope
What is a finderscope?
A small low power telescope mounted alongside the main tube, used to find objects before looking through the main instrument.
Red dot finder or optical finder?
A red dot for speed on bright objects, an optical finder for star hopping to faint ones. Many telescopes carry both, and they cost little.
How do I align a finder scope?
Centre a distant object in the main telescope in daylight, then adjust the finder until it points at the same thing.