Apartment guarantor process

I must find my own apartment, but my company will sign as the guarantor.
How does the process work?
Can I make appointments to view apartments on my own?
When I'm filling out paperwork for an apartment, does someone from the company have to be present?
Or do I take papers from the realtor to the company and then back to the realtor?

I would suggest you ask your company.

But I am pretty sure that no one from your company will want to come along for visiting the apartment. Just search for one and once you found it you will need the guarantator.

Enjoy your life in Japan!

Things depend a bit on factors like: if you speak the language enough to explain the situation; if your employer knows an estate agent (or two) that they've worked with before with their employees; and what kind of budget you are talking about.

It might be easier if you and someone from the company went to a real estate agent together first, just the first instance, to get yourselves acquainted with the agent, get the company staff to say that you are/will be their employee, and that you'd like to rent a place (of approximate size and budget maybe), and that they will be the guarantor. For individual appointments afterwards (provided you stick with one agent) you can go on your own.

For the paperwork, you might want to take their contract back to your company once for them o review it closely. But if the company has experience being a guarantor for non-Japanese employees, they might not need it.

I am not fluent in Japanese, but my best friend is Japanese and offered to help me through the process. I guess my question is, how does someone physically sign as the guarantor? How do I prove I have a guarantor? Do I need to bring paperwork from my guarantor? Does the guarantor have to be present when signing/finalizing the paperwork?

Probably it would work like: you get the final version of the contract at the estate agent, the landlord part filled in & signed, and they either ask you to take the contract back to your employer to have the guarantor part filled in and stamped, or they give you a separate document "letter of guarantee" to take back to your employer to fill in & sign/stamp. (You can have either your friend or your employer to check the contract in detail so you can sign it. )

When it comes to "proving" that you have a guarantor, ask at your employer's HR or Admin section for a business card from one of them in charge of employee's housing (in case you don't have your business cards printed yet) and show it to the estate agent as your employer. The estate agent, if they want to make sure, they can call your employer to ask.