To illustrate, here’s a demo.
We start off with a generator point P that is known to everyone, since that’s built into secp256k1’s specification.
To add P with itself, simply take the tangent at the point P. Where the line intersects the curve let’s call it -2P.
We then reflect this point across the x axis, resulting in our answer 2P.
To get 3P, we can add P to 2P via the same process.
Draw a line through P and 2P, find where they intersect, which is -3P, and then reflect that across the x-axis again to yield our answer 3P.