First of all You won’t find here any information on high speed BLDC motor driving. For that purpose You need to know rotor’s position, so You have to measure back-EMF or use Hall sensors (not needed here).
For basic info about driving BLDC motors here is best “classic” articles on internets:
Driving a three-phase brushless DC motor with Arduino – Part 1. Theory
I used specialized triple half bridge IC L6234 (~ 8$). You can make the same spending less money (but more time) with MOSFET transistors or other IC.
But be careful, I found a lot of cases in various forums, where people burned their Arduinos or L6234 chips.
If You connect L6234 INputs directly to Arduino and OUTputs to low impedance motor – current from Arduino pins will be driven directly through L6234 to the windings and to the ground (without external Vs power applied to L6234). This makes very good chance to burn Your lovely microprocessor.
Also in application note, one sentence is worth to mention – “To avoid overload of the logic INPUTS and ENABLES, voltage should be applied to Vs prior to the logic signal inputs.”
I also very recommend to study (or/and purchase) this open hardware driver board based on L6234 BLDC Motor Driver by Michael Anton. It has input protecting resistors, zeners, power supply/filtering components and even back-EMF sensing circuit with amplifier (not used here).
For more detail: Spining BLDC motors at super Slow speeds with Arduino and L6234