Make a single loop with lines passing through the centres of cells, horizontally or vertically. The loop never crosses itself, branches off, or goes through the same cell twice. Lines must pass through all cells with black and white circles. Lines passing through white circles must pass straight through its cell, and make a right-angled turn in at least one of the cells next to the white circle. Lines passing through black circles must make a right-angled turn in its cell, then it must go straight through the next cell (till the middle of the second cell) on both sides.
Loop puzzles can be tricky and use different kinds of logic, but hopefully this walkthrough will help introduce some of the key ideas.
The walls can be good places to look. Black circles must make an L shape, so there must be a vertical line and a horizontal line of length 2. If it can't go up, it must go down. If it can't go left, it must go right. This forces the red lines shown. The white circle must have a line going straight through it, so it must go up and down.
This forces the white circle in the centre to go up and down since it can't crash the line on its right. It also forces the red line coming out of the black circle for the same type of reason.
My next reasoning is that the path through the white cell has to continue up because it can't turn before that, and since the black cell has to have length 2 cells coming out of it, it must go left as if it went right it would only be length 1.
For the loop to continue from the white circle, it has to go all the way along to the right and has to connect with the existing loop section. At the bottom, it has to turn because it has to turn in one of the adjacent cells, and it hasn't turned in the top cell. The bottom right white circle had to go straight, so that could have been continued down at any point up until now, really. The very top left cell of the grid must continue along the loop and hence go down.
The left hand white circle hasn't had its turn yet, so it must turn below. The right of the two adjacent white circles can't go up and down, so it goes left and right, which forces the other one to go left and right too.
For the loop to close, the loop sections must join as shown.
