A pair of plastic nippers. NOTE: do NOT use scissors! This can damage the parts. Certain kits can have their parts plucked out by hand - but the kit will tell you if that's the case.
A tool to remove "nub marks" - the marks left over after a part is removed from the runner. This can be a simple as a nail file or fine grit sandpaper - or even up to specially designed nanoglass files.
And that's it, really! Some people like to paint their kits with an airbrush, or do what's known as panel lining, but all you need is a proper way to remove the parts, and the instructions for the kit - always included.
"That's all well and good, but what do I do? There's so many runners!" Fret not, the instructions on genuine gunpla kits are of high quality.
Each step is labelled with a runner's letter and then the part's number. Just find the right runner, and then the right part, and carefully nip the part off the runner at each "gate".
Once a part is removed, carefully use your nub mark tool of choice to carefully remove the mark. If you cut a little far, don't worry - just use the sharp end of your nippers like an X-acto knife. Once you're down to a small dark spot - you're good!
"But wait, what is that spot anyhow?
It's simply excess plastic color left over from the injection process, and there's no way to remove it without paint. If you're left with scratch marks, simply get a finer grain tool and go over it again. To polish, use a microfiber cloth.
Do the same for every part in a step, panel lining if you chose to, and then simply press fit together!
WARNING: some parts in a step are labelled, e.g. 1, 2, 3. Attach those parts in order exactly! Otherwise you might be unable to fit a part, or even snap them!
In short:
Step one is to identify your part via letter and number.
Step two is to cleanly remove the part with your nippers.
Step three is to remove nub marks with gentle abrasive of your choice.
Step four is to put the part onto the kit! Or move on to the next part in the step if there's nothing to attach yet.
Just follow those steps according to the instructions and you'll have your very own gunpla built in no time!
Glossary of terms:
Gunpla
-- A brand of model kits representing the mecha from Mobile Suit Gundam. Short for "Gundam Plastic Model.
Nippers
-- Any tool used to remove parts from injection-molded runners
Runners
-- Also known as sprues, are what each Gunpla kit uses to hold parts before assembly. Each part is held on with one or more gates.
Panel Lining
A technique of using thin paints to accent built-in lines on each part, to add visual interest.