Picture of How to Add
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.
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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

Picture of 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

Picture of 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

Picture of 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