Measure amps with MCU

I want to power a high power LED. I figure I could use a MCU and 50VDC, transistors... but how does one measure current?

If you have no idea what the current you are measuring is, I would suggest using a multi-meter with current measuring capability. If you want to measure a specific current value in a known range of values, there are a number of application notes from semiconductor manufacturers that explain the process.
TI - Simplifying Current Sensing
TI - Low Side Current Sense Circuit Integration
TI - Low Cost Bidirectional Current Sensing Using INA181
Microchip - Current Sensing Circuit Concepts and Fundamentals
Google "current sensing application note" for more information.

mattlogue:
I want to power a high power LED. I figure I could use a MCU and 50VDC, transistors... but how does one measure current?

"A high power LED" - what LED exactly?

The current capability of the transistor is the most important part of your selection. The voltage only has to exceed the maximum circuit voltage. Consider using a MOSFET, the voltage drop across it will be much less and it will run cooler. A cheap and dirty trick is to simply measure the voltage across your series resistor and using ohm's law calculate the current. Most current meters do this in one form or another. This response is to help you get started in solving your problem, not solve it for you.
Good Luck & Have Fun!
Gil

What do you have against using a dedicated LED power supply, one that's designed to do just this job?

I want to power a high power LED.

This is insufficient information.
When discussing current , you need to specify the magnitude of the current in amps.
Without this info, it's like asking what kind of carburetor to use on a car without saying
what car or how much horsepower you need.
DC current can be measured using current sense resistors (0.1 ohm/1W) or current shunts
(rated by maximum amps). If you place these between the load and GND, then the voltage
drop can be measured by the arduino across the resistor or shunt as an analog voltage.
For example 5A x 0.1 ohm = 0.5W, so this current sense resistor could measure up to 10A (P = I X V=> 10A x 0.1 ohm= 1W).