How to visit Georgia as a Pakistani citizen?

With Pakistani passport, you do need a visa to visit Georgia. Unfortunately, I'm having hard time finding anything useful on the website of Ministry of Foreign Affairs of Georgia and, hence I'm not able to confirm whether visa on arrival is an option for you (it is for citizens of many countries).¹ You can try calling the border control in Tbilisi Airport on +995 322 418515 and ask them.²

Other than that, you can always apply for your visa before travelling. As you're in China, you can start with the Georgian Embassy in China:

Website: http://china.mfa.gov.ge/
Address: 18 Xiaoyun Rd, Chaoyang, Beijing, China
Phone number: +86 10 6468 1203
Consular hotline: consulinfo@mfa.gov.ge

Unfortunately, the link to visa information on that website returns 404 (not found) though.

If you prefer to apply from Pakistan, then it's worth noting that there is no Georgian embassy or consulate in Pakistan. Instead, the embassy in Tehran (Iran) handles all Pakistani-related matters, including processing visa applications. Here are the contact details for the embassy in Tehran:

Website: http://iran.mfa.gov.ge/index.php?lang_id=ENG&sec_id=330
Address: ?92, 2nd Golestan st., Pasdaran Ave., Tehran, Islamic Republic of Iran.
Phone numbers: (+98 21) 22 76 41 29; (+98 21) 22 78 23 89; (+98 21) 22 78 23 86;
Working hours: 9:00 - 18:00
E-mail of the Consular Section: tehran.con@mfa.gov.ge

Unfortunately, the link on that web site to the visa information is also broken, resulting in 404 (not found).

Last, but not least, you may be eligible to apply for eVisa, which was introduced by Georgia recently. More details are available on the eVisa web site here: https://www.evisa.gov.ge - however there are specific restrictions for citizens or residence of Pakistan, namely:

Citizens and stateless persons permanently residing in one of the countries listed in this paragraph [Pakistan is one of these] are required to be in possession of a valid supporting document (Schengen visa or a valid visa from any of the OECD member countries; or a valid residence permit of a Schengen or OECD country) to be eligible for Georgian e-Visa.

At the same time, as you reside in China, probably this paragraphs applies to you rather than the first one:

Citizens and stateless persons permanently residing in one of the countries listed in this paragraph [including China] are required to be in possession of the documents listed in this section...

Have a look at the specific requirements: https://www.evisa.gov.ge/GeoVisa/Countries/Index.html

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¹ Here's the general visa information page on Georgian MFA site: http://www.mfa.gov.ge/MainNav/ConsularInformation/VisaInfoForeign.aspx - but I couldn't find much useful information there. Overall, their site isn't very well organised, in my opinion.

² Tbilisi airport contact information can be found on their web site here: http://www.airport.ge/Tbilisi-Airport-Contacts.html