For 3.3V microprocessors, what's the best way to power the gate of a MOSFET?
Three options.
Use a mosfet with a VGS compatible with 3.3V. Typically known as a logic level mosfet.
Use a simple npn transistor as a switch to drive the mosfet at a higher voltage. Logic would be inverted.
Use a dedicated mosfet driver IC.
Assuming you only have 3.3V available, that your MCU can supply at least 1mA thru the gpios, and that your application does not require more than 10A, I would use a N mosfet compatible with 3.3V.
For example the PMV16XNR has an On-Resistance of only 20 mOhm when powering the gate at only 3V, and can source a bit more than 6A. There are many other compatible MOSFETS.
Just be careful to add a resistor from your gpio to the gate, so the current spikes when switching the mosfet are not too large. For the PMV16XNR I use 500 Ohm resistors before the gate so the spikes are 6mA and the maximum switching frequency is somewhere near 300 KHz.
If using this option remember also to put a large resistor from the gate to ground, so it is powered off if gpio is floating.
If you need a much bigger MOSFET, then a mosfet driver or a charge pump could be necessary.
If you tell us your application and more details, maybe we can help you better.
For P-channel FETs, another option is to use a combination N/P MOSFET device. These have both P and N FETs built into the same pacakge. The P can be used as the high-side switch and the N can be driven at 3.3V to turn the P on/off. For example, SI4559ADY-T1-E3.