What is the crafting recipe for a powered rail?
In a crafting table (3x3), place gold ingots down the left and right columns (6 total), 1 stick in the very center, and 1 redstone dust in the bottom-center slot. This crafts 6 powered rails.

How do I power them?
Powered rails only boost when they get a redstone signal. Easy options include a lever next to the track (constant power), a redstone torch placed on a block beside or under the rail so the block powers it (not on the rail itself), or a button for temporary power.
Quick range tip: a single power source can usually power a short run of powered rails in a row, up to 9 rails in many setups. After that, add another torch or lever to keep the boost going.
How far apart should powered rails be?
Use this as a simple starting recipe: place a powered rail to launch, then add another powered rail whenever your cart starts to feel sluggish. On flat ground, you can space them out. On uphill sections, place them much closer and make sure those uphill rails are powered.
If you want a concrete build rule: power a run of up to 9 powered rails, then repeat with another power source as needed.
Do powered rails work as brakes?
Yes. A powered rail that is not powered will slow and stop a minecart, which is perfect for stations. A normal rail does not actively brake the same way.
Can powered rails go around corners?
No. In vanilla Minecraft, powered rails cannot curve. They only place straight (or as an incline). Use a normal rail for corners, then put powered rails on the straight stretches before or after the turn so you keep your speed without turning your station into an accidental stop sign.
Do powered rails speed up faster than normal rails?
Normal rails do not speed you up on their own. Powered rails are what give you acceleration and help maintain speed, especially after turns, bumps, or small elevation changes.