You actually won't necessarily cut the new fork to the same length as your old fork, because your new frame may have a different head tube length.

to cut the fork and install the frame you will need:

a new threadless headset
your new stem
any spacers you plan on using
a crown race slide hammer (see below)
a hacksaw
a steerer tube cutting guide

Here's how it works:

First you will need to install your crown race.

the best/cheapest way to do this is to find a length of pvc pipe with an inner diameter that will just slip over your steerer tube.

make a perfectly square cut on the end of this pipe, and use it as a slide hammer to seat the crown race on your fork (be careful to ensure the the race doesn't go on crooked) You can also purchase a specific tool.

The process of installing the headset races is one you may want to take to your LBS. With the correct tool, it is a snap, but especially with a new frame, which may need some prep work, you might want to have them do it.

if you still want to do it yourself, here is what I recommend:
either purchase a headset cup press, or manufacture your own, using a 24" piece of 3/4" threaded rod, two nuts, and two washers.
You will need two 10 mm headset spacers.
stack as follows:
nut
washer
spacer
top race (lightly greased)
frame
bottom race (lightly greased)
spacer
washer
nut

Center everything and ensure that the spacers are pressing on the flat at the base of the races, and that pressure is not being applied to the raised rim of the races.
slowly tighten until both races are snug against the frame.

if the races resist seating, don't force it - your frame may need to be prepped to the proper diameter to allow the races to seat properly.

At this point you can stack everything up in order:
fork(with crown race)
bottom bearing
frame (with races installed)
top bearing
top bearing race
spacers
stem
spacers (optional)

mark the steerer tube at the place it emerges from the stem, or top spacers

cut the fork using the cutting guide about 2-3 mm below this mark.
if it is a carbon steerer tube, you will need an expansion plug (otherwise you use a star-nut)
The cutting guide isn't obligatory, but it certainly helps your peace of mind, and it's not all that expensive.

re-assemble the entire stack, install the top-cap and screw, and tighten to the torque setting recommended by the headset manufacturer. (or until there is no play in the headset)
then securely tighten the stem clamp screws and you're all set!

this info is also on the Park Tool website, and I'm sure it's on Sheldon Brown as well.

Note - it may be good to plan on using extra spacers above your stem, in case you find your handlebar placement needs tweaking later. However if you're sure of the geometry, they are completely unnecessary.