Reading the clues
Each number is a run of filled squares in that row or column, in order, with at least one empty square between runs. A clue of 3 1 in a row of 10 means a run of three, a gap, then a single square.
The overlap method
Imagine the run pushed as far left as it can go, then as far right. Squares covered both times must be filled. In a row of 10 with a clue of 7, the run covers squares 1 to 7 on the left and 4 to 10 on the right, so squares 4 to 7 are certainly filled.
A quick test: if a single run is longer than half the row, some of it can be filled straight away. For several runs, add the runs and the gaps between them: 4 3 needs 4 + 1 + 3 = 8 squares, leaving 2 spare in a row of 10, so the first run certainly fills squares 3 and 4, and the second certainly fills square 8.
Use the edges
A filled square at the edge of the grid must start a run. If the first clue in that row is 3, the next two squares are filled and the one after is empty.
Mark what is empty
Once a row's runs are all placed, mark every other square in it as empty. Empty squares are as useful as filled ones, because they limit where runs can go in the crossing columns.
Switch between rows and columns
Every square you fill or empty gives new information to the line that crosses it. Work back and forth until the picture appears. Every puzzle in Nonograms can be solved this way without guessing, including the daily puzzle.