What is the best way to prioritize a to-do list?

Colour coding according to subject, numbering based on due date/importance.

By “prioritize a to-do list” I think you mean prioritizing the items on the list, not making one.
I put myself in a situation where I can focus, if my to-do list is course work. If it’s Chores I turn on a show I’ve seen a thousand times and I clean while it’s on. It helps me not feel bored. It can be difficult for me to prioritize, since I am disabled and my symptoms make it hard to garauntee plans in advance.
Making it so I can only do the thing I need to do, like going to the library

Put priorities first to get important things out of the way. Follow the to-do list almost religously if you can. Have the list always visible for a quick reminder.

I do Tony Robbins RPM method to build a goal of how I want my day to look them design task around my goals.

My way is first creating priority groups (for example A, B and C) and then prioritize only inside priority groups (assign numbers for them for example). This way I will have a list like that:
A1 Talk with X
A2 Buy bread
A3 Call Y
B1 Buy Presents
B2 Clean up
C1 Watch Avengers
C2 Practice chess
C3 Go shopping

This is a fast and easy way for me.

I'd suggest to make a "To do Master list" first where you write all the things you need to do in the next few days and pick items from that list to put on your regular to do list (or as I like to call it, the "To-day list"). You should make the decision of what to put on your to do list considering the importance and urgency of the tasks first. For example some tasks are very important but they don't have a deadline attached so you might find yourself postponing them indefinitely. Make sure to put these on your list as well and try to deal with them as early as you can in the day so as to prevent overfocusing on the time-bounded tasks later on in the day.

I try to pick the three things that are most important, most urgent, and most efficient if done today. Don't get tricked by deadlines- if today is the last chance to do something, but it's not actually important, you don't have to do it at all. If something is important, I love to get it done early, but see if there's anything else that is important and needs to be done first. And if it just doesn't make sense to work on it today- my homework is due in a few days but I'm too tired to do it well, or I need groceries but I can stop on the way home from work tomorrow- pick a different day.

Highest priority are items with deadlines coming shortly, things I may have avoided or put off, and things with dire consequences for not being done.

Lowest priority are things that would be nice to get done but not really important, or things I don't want to forget about.

The piece of this answer that tends to be overlooked or skipped, probably because it's assumed to already done, is your personal values. This is where the middle variances of priority come into play for me. I'll use myself as an example.

I value my family above all. I'm going to school to improve my situation. This is my secondary priority. Work is a tertiary priority in this case.

A family item that's not crucial might be a step above the lowest level. School deadlines are probably going above most family items… except family deadlines or work deadlines that could cost me my job.

I currently work with four levels of priority. Items can fluctuate priority based on the above criteria.

Hope this helps. Good luck!

According to your most valuable priorities. Then filter through: Delete->Automate->Delegate->do it or purposefully procrastinate

Don't think "should"…just focus on the 3 that must be done today, then schedule your other days so all you have to think about is TODAY. It can get overwhelming so keep it simple and be proud of yourself for every little thing you check off.

I separate my to-do list into categories and then look at what is most important in that category. I then try to accomplish just those important tasks for that day.

Do your “musts” first, then do your “shoulds”

Do it first thing when you start to work. Set aside 2 full hours before you do anything other then what is on your list.

Consider when things are due. Which due dates are earlier in the day/week? Which are later? Focus on each thing on your list. As you go through each one, thinking about only that one, ask yourself "What would happen if I did this tomorrow/next week, instead of doing it today?" Is the answer good, bad, or neutral? Note the answer G, B, or N for each item. When you're finished, see which ones are B's. These are the ones you've selected are most important to do right away. If you've selected too many to do in your allotted hours, go back to your shortened list again and think through each of them as you did with your original list. If you still have too many after that, reach out to people who many need the results of that task about needing more time to do a good job. People are understanding. 😊

I like to identify everything I have to do first. Then from there I like to pick something that will be an easy win right away—that helps me “work up to” a bigger item on my list that’s either been a real roadblock for me or I just don’t want to do it. When I do get to the bigger/harder items, I often set a timer and tell myself I can take a break only after the timer goes off. The time I set depends on how much I’ve been resisting that thing—I have a project today that I’m going to time in 10 minute increments. If I get to the break and feel like I can keep going, I always do. Usually I find once I get myself started, I find a stride. But if I’m getting to a point of frustration or boredom, I’ll take a short active break (walking/stretching) just to let my mind reset.

İn my opinion, the best way to prioritize a to-do list is categorizing them based on some groups such as, due to deadline, it is mandotory or optional, duration (it is daily task or we have enough time for to do it)

First I write everything down in no order as it comes to my mind.
Then I pick the top 1-3 tasks and put them at the top in order of importance.
Then I write down times in 30 min increments and out the tasks from the original list on the new list in the time slot that would work best for my day.

In the evening, before bed, I write down all the things that need done the next day. This keeps me from thinking about them so I can get to sleep easier. In the morning, I take that list and combine it with anything that might be on my calendar for that day. I also add anything that was not accomplished the previous day, has just come up, or that I forgot. Then I prioritize using the A, B, C method. Giving each letter three tasks.