If you can capture a piece, you must. Every formal version of checkers uses some version of this rule. If you're not used to it, I think you'll be pleasantly surprised with how much forced captures add to the challenge and beauty of the game.
Offensively you can compel your opponent's pieces onto weak squares or force your opponent to open their back row. And defensively you can trade off your opponent's most dangerous pieces. This site is designed to help you practice seeing these tactics.
Try one here.
Kings may move diagonally forward or backward one square and capture forward or backward by jumping over an enemy piece and landing in the empty square behind them.
There are popular versions of checkers where kings may move many squares along the diagonal and capture by jumping over many empty squares. Usually in these versions pieces can capture backwards. These versions are fun and I hope to support them some day but in English Checkers kings are slow and pieces capture only forward.
In many places on this site and elsewhere you will see little data blocks that look like '11-15' . These are descriptions of moves and in this case say, 'The checker on square 11 moves to square 15'.
'11x18' describes the checker on square 11 capturing the piece on square 15 and landing on square 18.
'11x25' describes the checker on 11 landing on 25 and capturing pieces on 15 and 22.
Most of the time on this site you can click on the description and see what the move looks like. The square numbering system takes a long time to get used to but it's the standard. In the future I'd like to support the chess notation as well because many people are more familiar with it.
For a complete explanation of the rules check the wikipedia page for English Draughts.
If you're playing at home, and I hope you do, consider these ideas to maximize your enjoyment.
Either player may at any time and for any reason resign to end the game with a loss. This is not considered poor sportsmanship and can help avoid the frustration in playing out a hopeless position.
If both players agree, the game can be declared a draw at any time. Start a new one and maybe try a different opening.
Use a chess clock or download an App. If your time runs out you lose! The shorter the time, the sillier it gets. Try anywhere between 1 minute and 45 minutes per player. You can also give the weaker player more time to think to keep things fair.
The proper move order is to crown the enemy piece if appropriate, make your move, remove any captured pieces, then hit the clock. It should all be done with the same hand.
If you can capture a piece, you must!