Matchlock.

The musket was loaded using a small containter (often in waterproof leather to protect the gunpowder from moist and water) that had the correct amount of powder pre-measured. These would often hang from a bandolier of the musketmen of the era. A tallowed or greased up patch of cloth or or ball of yarn or similar would then be inserted, then the ball and then another tallowed or greased patch or cloth.

These two patches had the purpose of fixing the bullet in the barrel (there could be consideable difference in the calibre of the bullet and the barrel) and protect the gunpowder against moist and water which could cause the musket to misfire.

The musket would have a small pan on the right-hand side at the bottom of the barrel with a small tube to the chamber where the gunpowder charge was. This small channel and pan from which it emerged would be filled with gunpower.

A fuse, glowing, would be fixed to the cock, the cock would be cocked and released with the press of the trigger. The fuse would end up in the pan, lighting the gunpoder there. This ligth woudl travel down the gunpowder in the small channel and ignite the main charge, and the musket would discharge its ball.

Flintlock

Exactly same as the above, except that the pan would have a L-shaped lid and instead of a lighted fuse on the cock, there would be a piece of flint.

When the trigger is pressed, the cock goes forward and the flint strikes the L-shaped lid, throwing it back and exposing the pan, while sparks would be created by flint striking steel and rush down into the pan, igniting the gunpowder.

Protecting the pan with a lid made the musket much more reliable in bad weather, and allowed you to keep the pan filled with gunpowed, meaning you could keep a shot ready to go.

Other advances

While the flintlock musket improved both speed of fire and reliability, there were also other advances that made it superior. Greased paper rounds were manufactured and distributed - the musket ball and the gunpowder were joined together in one package. The greased paper protected the gunpowder against water and moisture. This technology was used until metal casins for rounds were introduced from the 1800s. I am sure you have seen movies of the US Civil War, where soldiers bite their paper rounds to open them, pour the gunpowder down the barrel and then put in the bullet (greased paper and all) and ram it down the barrel with a metal ramrod.

The greased paper also served the same role as the patch of greased cloth had done, but was ready immediately, shortening reload times.

Interestingly, the rumour that the British were greasing their rounds with pig's fat played a part in the Sepoy rising in India, as pigs were unclean for muslim soldiers. The British were most likely using only sheep's tallow since cows were holy to Hindus and pigs unclean to muslims.

The iron ramrod, which was introduced in the 1740s and the Prussians pioneered (allowing Frederick the Great's infantry to reload faster) allowed quicker and harder movements without breaking, making reloading quicker than with the earlier wooden ramrods.