Crosshatching is the technique you use before you use any technique. It needs no pencil marks, it's almost entirely visual, and on gentler puzzles it will fill in fifty cells before you have to think hard once.
Every digit already on the board casts a shadow. A 5 sitting in row 3 means no other cell in row 3 can be a 5; the same goes for its column and its box. Pick one digit, look at all of its existing placements at once, and mentally sweep those shadows across the grid. Any box where exactly one cell remains unshaded has just told you where that digit goes.
In the diagram, we're hunting 5s in the top-left box. The 5 in the first row blocks the top three cells of the box. The 5 in the second row blocks the middle three. That leaves the bottom row of the box — three candidates. Then the 5 in the first column knocks out the leftmost of those, and the 5 in the second column knocks out the middle one. One cell survives. It's a 5, with certainty, and it took no writing at all.
Scanning at random is slow and you'll miss things. Two disciplined orders work well:
Take 1, and check all nine boxes for a forced placement. Then 2. Then 3, and so on to 9. This is thorough, and it has a natural stopping point — when you've been through all nine digits without placing anything, crosshatching alone has run out and you move on to pencil marks.
Faster in practice. Count how many times each digit already appears and start with the most common one. A digit that appears seven times has only two cells left to find and they're hemmed in from every direction. A digit that appears twice is unlikely to resolve yet and isn't worth the sweep.
Every digit you place changes the picture for twenty other cells — eight in its row, eight in its column, four more in its box. So after a successful placement, don't carry on down your list. Go back and re-scan the digit you just placed, and any digit that shares a unit with it. Placements come in chains, and one found 5 will frequently unlock the next 5 immediately.
Most people learn crosshatching as a box technique and stop there, which leaves a lot on the table. The identical logic works on rows and columns.
Take a single row and ask where its missing 4 can go. Cross off cells in columns that already contain a 4, and cells in boxes that already contain a 4. Frequently one cell is left. This catches placements that box-scanning misses entirely, because the constraint arrives from three different boxes at once rather than from a single dense neighbourhood.
A useful habit: when a row or column has only two or three empty cells left, stop scanning by digit and just work out what's missing from it. With two blanks and two absent digits, a single conflict check usually resolves both.
Crosshatching runs dry — always, on anything harder than Easy. The signal is a complete pass through all nine digits with nothing placed. That is not a wall; it's a handover. It means the remaining deductions depend on relationships between candidates rather than on elimination by presence, and for those you need the candidates written down.
Turn on Notes, fill in the pencil marks, and move to singles, then pairs.