As long as you have all of your certificates of withholding, you bring them to the tax office, plug the numbers into the right boxes, add your health insurance/pension payments to the right boxes (because surely you've saved all those slips too), I think if you have life insurance or earthquake insurance you can claim that, pick an appropriate number for the work-related expenses box (you probably wouldn't be able to claim anything for your full-time job but maybe your part-time job), add up all the columns, and pray you aren't taking too big a hit. You may find yourself pleasantly surprised to receive a refund.

Your local ward/town/city office will usually have a Tax Return Center set up, with plenty of assistants flitting around and helping people fill out their applications, laptop stations for people filing electronically, etc. If you live in a more populated area they will probably have a couple English speakers as well. I think this will be my 7th or so year of filing my own taxes and my level was below yours when I started (now it's probably N1 but I inevitably rope one of the helpers, wave last year's tax return at them, and say "I did this but with different numbers").

TBH, if you're working full-time at one company and they'll do the taxes for you, I would just give them the withholding slip from the part-time job and be done with it. But there's a few resources online for foreigners filing taxes in Japan, so maybe if you do the math you'll find that it's to your advantage to do it yourself.*

^{*IANAA - I Am Not An Accountant - and have no idea how taxes work for married couples here. YMMV.}