There are many low tech inventions, and conceptual frameworks that could turn the tide of a war or make a person rich.
The idea that you can understand the world through iterative experimentation comes from the enlightenment. This is a powerful framework in which to work.
Constructing a simple bicycle requires a decent knowledge of ironwork. An army equipped with bicycles could cover 100 miles in a day and arrive fresher than an army which has marched the same distance.
Construct a battery from steel and copper plates plus lemon juice. stack enough of these together and you might even be able to create an arclight.
Cast iron is brittle. The addition of Carbon atoms, readily available from wood makes iron much stronger. Take your molten iron and chuck in some branches. Presto, your swords are sharper and stronger than the warlord next door.
Generate electricity by spinning a magnet in a copper coil. A piece of magnetite should do the job. This also possibly opens the way to induction hardening.
Navigation by compass
We don't know for sure when people first realised that a piece of magnetite floating in water would align itself north-south. It may have been as late as the 15th century. A magnetic compass would provide an obvious advantage to anyone wishing to navigate on a cloudy night.
Crossbows are simple powerful, quiet weapons. The man who invents the crossbow would be put in charge of many things.
Kites are simple to construct. A large enough kite can carry a man, giving a medieval warlord superior scouting capabilities.
The Romans knew about this, it's not hard. Have a slave heat water in a boiler, then pump it under the floor. A nice warm house for a nobleman.
Water can be transported from place to place via a lead pipe. A low tech solution that makes a fashionable nobleman's life better, until he goes mad from lead poisoning of course.
Medieval codes were simple substitution cyphers. A modern person with a basic knowledge of probability ought to be able to crack such a code with ease, and could easily come up with a stronger code.
Medieval ships had square sails which meant they could only move if they had a following wind. More modern ships have a triangular sail with a swinging boom, plus a deep keel. This means they can sail across the wind and tack into the wind. The advantages here in terms of warfare and commerce are obvious.
A mechanical loom can be constructed from wood. With a little thought our modern human might be able to work one out.
Ball bearings dramatically reduce the friction in a wheel. A coach or chariot equipped with ball bearings can move faster with the same number of horses.
Stagecoaches used a large metal spring on which the coach itself was suspended. A simple innovation providing greater comfort for travelling royalty on bumpy roads.
Slightly trickier this one, but presumably long sightedness among older people was an issue in the middle ages just as it is today. Glass was available in medieval Europe. Given time and persistence it could be shaped into a convex lens of great value.
A convex lens can also be used to start a fire in sunshine, which presumably would have looked like the most extraordinary alchemy.
A large concave mirror made of polished metal can concentrate the sun's rays on a target, perhaps a ship, a siege weapon, or an enemy general. A burning glass may have been used by Archimedes as early as 212BC. Of course you would need sunshine for it to be effective.
Books were expensive. The concept of movable type would not be hard to replicate. A person with a printing press could be rich.
An oil soaked rag in a metal box, plus a flint and steel. Magic instant fire in the palm of your hand.