I think the only real reason to become more assertive is, primarily, so people do not walk all over you. be that your boss or in personal relationships. Being able to state, firmly and clearly but diplomatically, what you are and are not willing to do etc. Being able to speak up in say a restaurant if your food is not served as you requested or other daily annoyances is important too, but really….it all comes down to picking your battles. If someone is annoying and you are not invested in a working or personal relationship it is best to just let their annoyances go and move on.
Start with simple things like practicing speaking clearly and at a volume you can be heard. Do not speak softly or mumble and make eye contact, very important. Direct eye contact is an assertive and confident gesture that conveys confidence as @Cruiser mentioned.
If your burger is soggy and your fries are cold at the drive through, don’t be pissy about it and fume but eat your crappy lunch anyway. Drive back through and say ” My burger is soggy and my fries are cold and I want a replacement meal.” haha
If someone cuts in front of you in a line, speak up, say ” excuse me but I am next.”
Once you get more comfortable with the little things you will have more confidence to tackle the bigger issues. Always stay calm, getting emotional and hysterical takes away your power, much better to remain calm, state your issue and don’t lose your cool.
Assertive is firm but calm and aggressive is sloppy and loud.