Patterns you NEED to know!

Starting a mini series called: Patterns you NEED to know and here's the first one.
Middle Pawn + King end game!

This will work with ANY Pawn on the b, c, d, e, f, and g files

Actual Patterns to memorize:
Opposition - When their King is on the same file as your Pawn, you must block with your King by putting it in front of theirs.
How to make forward progress - After opposition, their King needs to go left or right, that's our cue to go up one square and the in the opposite direction of their King. If they go left, we go up one and right one.
Making a Queen - after these two patterns, your King will land on e6 and we can finally start pushing our Pawn up. Once we get behind the King, we can push the King to d7 or f7 which protects the Pawn the rest of the way

Side pawn + King end games
are ALWAYS a draw - if you can catch or get in front of the Pawn in time.
This works for both White and Black.

Actual patterns to memorize:
Stop that Pawn - We want to get our King on the same file as the Pawn for as long as possible.
Opposition - if we're ever in a position that we're forced to move off of the Pawn's file, we will take the square that's the opposite of their King. Opposition is not as important as generally, the only time we use it, it's usually the only legal move anyways.

Rook + King end games are ALWAYS a WIN - if you don't lose your Rook!
This works for both White and Black.

Actual patterns to memorize:
Cutting off the King - We want their King to be as limited as possible with their moves. Using our Rook to make sure that they have as limited squares as possible.
Pushing our King - We NEED to use our King in order to force their King into a position so that we can deliver Checkmate. Using your King is crucial but make sure to not blunder your Rook if it's under attack.
Dealing with attacks - Simply, move your Rook as far away from their King as possible while staying on the same rank (or file, depending on how we're planning on Checkmating {stick to ranks until you're comfortable enough in your Rook end game to use the file if it's faster}).
Patterns over faster Checkmates - There will be times where there are better, faster Checkmating moves, but please learn the patterns and principles first. You should be able to always win with a Rook regardless of a move or two difference in Checkmating.

I wanted to add to the 'Rook + King' one starting in a different position but all of the patterns/ideas are the same.

Differences in patterns: Cutting off the King - We still want their King to be as limited as possible by using our Rook to make their 'cage' as small as possible. We do this until we get them on the end files or ranks.
Pushing them into a corner - Once their King is on an end file or rank, we can use our King and Rook to continuously make their space as small as possible. It's usually a combo of 2 King moves to protect our Rook while forcing their King down followed by 2 Rook moves to make the space as small as possible.
DO NOT STALEMATE - Once their King is in (or even close to) a corner, make sure they always have 2 squares that they can alternate between. Our King should be holding back any escape squares so those 2 squares need to be on the same file or rank as their King is currently on.
DO NOT CHECK - there is no need to EVER check their King unless it's a Checkmate. If you end up checking their King, they will probably escape their 'cage'. This seems a lot harder than it actually is but with a little practice and understanding of keeping their King in a box, you can easily win all of your Rook end games.

Queen + King end games are ALWAYS a WIN - if you don't lose your Queen
This works for both White and Black

Actual Patterns to memorize:
The "L" shape - Using our Queen, we must cut off their King and force them to an edge rank or file. By placing our Queen just outside of their King's reach, we can do this easily. To do this, use an "L" shape to help place your Queen. Think of how a Knight moves.
King on the Edge - Once their King is on an edge rank or file, abandon the "L" shape entirely. If you continue to do this, you may accidentally stalemate. We need to use our Queen to keep them trapped on the edge. You must place your Queen on the rank or file above their King so that their King can't leave.
Pushing our King - After they're trapped on the edge, we must bring our King into the action. Push your King as close to their King as possible. Once they're facing each other, use your Queen, bringing it face to face with their King (while being protected by ours) to deliver Checkmate.
DO NOT STALEMATE - Once their King is on an edge rank or file, make sure they always have 2 squares that they can alternate between.
DO NOT CHECK - There is no need to EVER check their King unless it's a Checkmate.

2 Knights + King end games are ALWAYS a DRAW - if you don't put your King in a corner.

This works for both White and Black.

Actual Patterns to memorize:
King in the Center - Move your King into the center of the board (d4, d5, e4, e5) and continue to circle that area.
Checks Aren't Scary - There is no FORCED Checkmate with 2 Knights and King, however, they can end up mating you if your King is in the corner. If you get checked, continue to move into the middle.

Here's the 2 Knights + King Checkmate. This is NOT forced and anyone above 1000 elo will know how to get a draw.

Bishop Pair + King end games are ALWAYS a WIN - if you don't blunder a Bishop.

This works for both White and Black.

Actual Patterns to memorize:
The Bishop Pair - A nice little trick is to always keep your Bishops TOGETHER as you move up the board with your King.
The Bully King - It may seem strange but your King is actually the pushing piece here. The Bishops create a net for their King to go. We will make that smaller whenever possible but a majority of your moves will be using your King to push their King into a corner.
King on the Edge - After their King is on the edge, we can use both Bishops on the 6th (or 3rd) rank to trap their King between 2 squares. Once they're trapped, use your King to prepare the checkmating corner (whatever corner is closest). You also want your King on the 6th (or 3rd) rank AND either the B or G files (depending on the corner) to help protect the Bishops.
Closing the Door - After our King is prepared, we can start to slowly push the King into the corner by placing our Bishops on squares that will lock the Kings previous squares. Just make sure that the King only has 2 squares to go to and it's headed into the corner.
King in the Corner - Now that our King protects the Bishops, it's time to deliver the first Check (again, depending on the corner you chose) but that check should force their King onto the square that's opposite our King. The checking Bishop and our King should actually prevent all escape squares, leaving our other Bishop to hit them with a Checkmate.
DO NOT STALEMATE - Once their King is on an edge rank or file, make sure they always have 2 squares that they can alternate between.
DO NOT CHECK - There is no need to EVER check their King unless it's the final check and then mate.

Queen + King vs King + Pawn (on the 7th rank) end games are ALWAYS a WIN.

This works for both White and Black.

Actual Patterns to memorize:
No Pawn Promotion - We CANNOT let that Pawn promote or it's a theoretical draw.
The Bully Queen - We have to use our Queen to do everything in our power to stop that Pawn. Pins, forks, checks, kicking around their King and guarding the promotion square.
The Traitor King - After their King is forced around, it will end up underneath their Pawn to protect it however that gives us one, free move so that we can bring our King into the action. You may have to repeat the bullying pattern a couple of times in order to bring your King as close as possible.
The King and Queen duo - After our King has arrived, close enough to help. We can shorten the original pattern a little bit and force the King underneath the Pawn a final time. Once that happens, we can use our Queen, protected by the King, to take their Pawn and force a Checkmate.
The Lone King - Using your knowledge of the King + Queen end game, trap their King on the last rank or file and bring your King close to deliver a final Checkmate.