Using Nano to run a string of 24V led strips.

Alright, so I have absolutely no idea what I am doing and this is my first arduino project but I have been scouring the internet for like 2 hours now trying to find an answer to this. I'm looking to run my fish tanks lights of a nano. I know this has already been done, but most if not all tutorials are for 12v or 5v strips. I already have a RGB W+WW strip that runs on 24V and I would really like to use that instead. So I realize that I need to use a mosfet in order to provide enough current to the strips, but my question is do I need to use a step up chip to provide the lights with the appropriate amount of voltage. I don't think I fully understand how mosfets work and surprisingly I can't seem to find the answer on wikipedia...
Thanks in advance.

You connect the plus of your ledstrip to the 24V.
The minus for each colour to the drain of the fets, the source of the fets to ground.
The gate of the fets go to the Arduino pins through a resistor (to prevent too much current).
And resistors from Arduino pins to ground.

Search for nick gammon motor; you can leave the reverse diode out and replace the motor by your ledstrip.

but my question is do I need to use a step up chip to provide the lights with the appropriate amount of voltage.

Yes, you DO need a 24V power supply. Typically you'd use a separate power supply or a dual voltage power supply.

The power supply needs to be rated for the "exact" voltage and at-least the required current. (The load will only "draw" the amount of current needed - Ohm's Law.)

What's the current rating (Amps or milliamps) for the LED strip?

...You could use a step-up DC-DC converter, but it's more than just a chip. Of course it needs to be rated for required output current. The 5V power supply would have to supply proportionally MORE current. For example, 24V at 1 Amp is 24 Watts. 5V at 4.8 Amps is 24W. That's (unrealistically) assuming 100% efficiency so you might need a 5V / 6A power supply.

[u]Here is a MOSFET driver schematic[/u]. You'll need a separate driver for each color.

Each color is 1/4 of the total current so the MOSFETs don't need the same current rating as the power supply, but leave some safety margin and you may need a heatsink if the MOSFETs get too hot. (You can burn-out a transistor or MOSFET at less-than-rated current if there is no heatsink or if it's not switched fully-on.) The voltage rating on the MOSFET shouldn't be an issue.... Any MOSFET should be able to handle 24V.

It's important to use a "logic level" MOSFET. Normal MOSFETs need more than 5V to fully turn-on and you're only getting 5V from the Arduino output.

You can leave the diode out of the circuit since your load is non-inductive.

Your schematic is no different from a 12V one, except that you supply +24V instead of +12V to the strip.

It should be a no-brainer to use a 24V power supply for that; you can use a separate 5V supply (e.g. a mobile phone charger) for the Nano, or a 24V-5V step down converter to use the 24V supply. In the first case make sure to connect the grounds.