Two basic rules
Every number is a count of mines among the up to eight cells around it. From that come the two rules that clear most of a field. First: if a number equals the count of covered cells around it, all of them are mines. Second: if a number already has that many flagged mines around it, every other covered neighbour is safe.
Apply them in a loop. Each new flag can make a nearby number satisfied, and each satisfied number opens fresh cells with new numbers on them.
The 1-2-1 and 1-2-2-1 patterns
Along a straight wall of opened cells, the sequence 1-2-1 is completely determined: the covered cells next to the two 1s are mines and the one next to the 2 is safe. The sequence 1-2-2-1 is its longer cousin: the cells beside the two 2s are mines and the cells beside the 1s are safe.
Both patterns follow from the second rule applied twice, so you do not have to memorise them, but recognising them saves time on medium and hard fields.
The subset rule
When the covered neighbours of one number are all also neighbours of a second number, compare the two. Say a 1 touches two covered cells, and a 2 next to it touches those same two cells plus one more. The 1 says one mine is among the shared pair, so the 2's second mine must be the extra cell.
This rule, subtracting one number's area from another's, is what medium fields here are built around. Look for it wherever two numbers sit side by side along a wall.
Counting at the end
On hard fields the last few covered cells may not be decided by any single number. That is when the mine counter matters: if three mines remain and a closed pocket can only hold three in one arrangement, the counter settles it. The solver behind each hard field allows this step, so keep the total in mind as the board empties.
Practice
Try the easy fields to drill the two basic rules, then the medium set for the subset rule.