Learn French: Je m'assieds sur la chaise.

It stands for me ('myself'). Just like waking up or washing, sitting down is treated as a reflexive action in French. The dictionary form is s'asseoir, which literally means 'to seat oneself'. Because assieds starts with a vowel, me drops its 'e' and becomes m'.

Assieds looks really unusual. Is it a regular verb?

Not at all! It is highly irregular. You just have to memorize forms like je m'assieds. Fun fact: there are actually two completely correct ways to conjugate this verb in French! You might also hear je m'assois, which means the exact same thing and is very common.

Are the letters 'd' and 's' at the end of assieds pronounced?

No, both the 'd' and the 's' are silent at the end of this word.

Can I use this verb without the m' if I am not sitting myself down?

Yes! If you are seating someone else, like a baby, you do not use the reflexive pronoun. For example, j'assieds le bébé means 'I seat the baby.' The m' is only there because you are doing the action to yourself.