This is my entry into the burning question, round 6.5.
I think that addition falls into the category of "Things that you should have learned in school, had you been paying attention", but for whatever reason, you are here.

Step 1: The Basics

One of the most basic properties of addition is that it is commutative. AKA it doesn't matter what order you add the numbers in, so long as addition and/or subtraction is all that you're doing.
that is to say that 50+25=75, and 25+50=75

And perhaps more importantly, addition is associative, meaning that you can add more than two numbers together and get the same result.
Which is to say that 25+25+25=75, and 15+15+15+15+15=75

But how does it happen? How do you add? I will try and explain it in the next few steps

Step 2: Adding Positive Numbers

All addition can be thought of as simply moving up and down a number line.
positive numbers push you up the line, and negative numbers push you down the line.

For instance, if you have "1+5", you start out at one and go 5 spaces up (into the positive area)
and you end up at 6. So 1+5=6. Alternatively, you could have started at 5 and moved one space up, also stopping at 6)

When you have 1+1+1+1+1+1, you start at 1 and then move up 1 space 5 times.
Stooping at six again.

And that is basically all that there is to addition with positive numbers.

Step 3: Adding Negative Numbers

Adding negative numbers is slightly more tricky, but not by much.
Adding negative numbers is simply adding positive numbers in reverse. Instead of going up the number line, you go down it.
For example, 0+(-4)+(-3)=-7

And after that, it's exactly the same as for positive numbers, only in reverse.

Step 4: Adding Positive and Negative Numbers Together

This is the most complicated part of addition, and even it's not that hard.

Adding a negative number to a positive number is exactly the same as subtracting a positive number from another positive number, or in other words: 5+(-5)=5-5=0
or 1+3+(-8)+2=1+3-8+2=-2, as in the picture

Step 5: Adding Numbers Together That Come Out to More Than Ten

So far, we have used a number line to calculate the answers to the questions. But what if you have 50+70? or 100+(-6)? it gets very tedious to try and draw a number line all the way up to 100, or even higher. Which is why I will show you the method for adding big numbers.

You start by stacking the numbers that you are going to add together, lining up the one's column.
Then you add all of the numbers in the right-most column together, and write it underneath your bottom-most number. You then do the to the column immediately to the left of the first column, and repeat this process until you've added all of the numbers together.

But what if two numbers add up to more than 9? in that case, take the the rightmost digit of the number and write it down underneath and carry the left most digit into the next column ad add it in there.

For instance in 87+150, 7+0=7, so that one is okay, but 5+8=13. Write the 3 underneath and write the 1 above the column immediately on the left of the column you just added together, in this case the hundreds column. And add it as if it were just another digit

Step 6: Adding With Variables

So far, all of the numbers we've added have been integers.
but what if you have variables?
such as x,y, or z?
when adding Variables, the line between addition and multiplication becomes blurred.
for example: Y+Y+Y=3*Y=3Y
When working with variables, just remember that:
1. unless you know the value of a variable, you cannot get rid of it
2. 2x=x+x, not x*x
3. y+y+x+x=2x+2y, not 2xy

If you need more pictures, or help clarifying anything, please comment on it and I will try to do something. I'm having problems with my image editor right now, so that's why the pictures aren't exactly 5-star right now

if you found this helpful, please vote for me, THANKS FOR READING!