sharps and flats -

Select the note, click the accidental in the accidentals palette.
Or use the up/down arrow.

See https://musescore.org/en/handbook/3/accidentals

Select the note, up arrow/down arrow. Does it work?

First read https://musescore.org/en/handbook/3/note-input paying particular attention to https://musescore.org/en/handbook/3/note-input#add-accidentals and also follow the link to https://musescore.org/en/handbook/3/accidentals

During note entry the basic process is

a.1. Select a duration,
a.2. Select an accidental in the tool bar if required
a.3. Type the note name on the PC keyboard (or click on the score to add the note at the desired line or space on the score)
a.4. If desired use CTRL+UP or CTRL+DOWN to shift the note an octave up or down

Or
b.1. Select a duration
b.2. Type the note name on the PC keyboard (or click to add the note at the desired line or space)
b.3. Use UP or DOWN (without CTRL) to repitch the note a semitone higher or lower. An appropriate accidental will be added.

If you are not in note entry mode you can add an accidental to a note by clicking on the note to select it and then clicking on the accidental in the pallet or in the tool bar or by using UP or DOWN to repitch the note as in b.3. above.

Generally, using the PC keyboard is far quicker and more accurate than trying to enter notes using a mouse.

When you have got the hang of that you may want to create keyboard shortcuts for accidentals. See https://musescore.org/en/handbook/3/preferences#shortcuts for how to do that (I use "-" for flat, "#" for sharp and "=" for natural, but you can decide what makes most sense for you.)

If you still have problems come back here and explain in more detail what you are doing, and what is not happening as you are expecting.