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
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
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 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
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