Yes, inviting someone out for lunch will build guanxi with them. Or, if that person asks you for a favor, and you do that for them, it will also build guanxi. By giving them face, by scratching their back, they will scratch yours. You don't have to be super outgoing, but being social is key to your success. You can still be honest, you don't have to use people, you don't have to compromise your values. They don't exactly see it as using each other, although sometimes it feels that way. If you do have guanxi with a person, they'll do whatever they can in their power to help you, although they may later ask a favor of the same magnitude from you in the future.

Unfortunately, sometimes being calculating as we would see it is the way to go. But as cat-woman above said, it's not seen as calculating here. Sharing stuff is a good way to start; bring some food into the office if you're working, share plenty of smokes around if you're a smoker, invite a bunch of people out for lunch and dinner occasionally, be generous with buying rounds of drinks (always!) and let them try foods from you home country (they almost certainly won't like your home food but that's not the point).

If you make people look good, that will be strongly in your favour.

What level of getting stuff done via guanxi are you wanting.  For around the office or in your normal day to day life then the posts above are great.  

If it's what I can "rainy day guanxi" that you need some extra strong pull or ability to namedrop if you got in trouble or had a major issue; then you'd have to start planting seeds of guanxi with important businessmen and government employees, by networking.  One of the easiest is knowing people that know people and sharing dinner and baijiu with those people.  

If you don't know someone that can get your foot in the door, then you'll have to be a little more outgoing and play the system some (the amount depends of where in China you are,  hint the more laowai in your city the less 'special' you are).

I'm a nice enough guy that I can even get you started.  Go to a nice resturant or KTV, and while your spending money and enjoying yourself, ask to speak to the owner if he is there (or at least the GM) because you want to toast him for running such a fine establishment.  Make this a regular thing (visit this nice place, exchange drinks and niceness with the owner) and he'll start to want to introduce (show you off) to some of his VIP guest.  Exchange toasts and business cards with them and BAM you got your foot in the door.  From there build the guanxi to whatever level you think you would need if you ever have to ask for the "rainy day" favor (if it's buying the table an extra bottle of baijiu to share with them, extra dinners, helping them or their family members practice english).

The key being you either have to have enough Chinese language to pull this off or have a friend/translator that handle remaining smooth and charasmatic because this could be a very unnerving situtation for him/her.

"Now I understand that who you know determines how far you can go. I get that. But it seems to be different here."

The main difference is that it's the only thing that determines anything. In the west your connections will get you very far, but if you don't do your job you'll probably get fired and if you kill someone you'll probably go to jail.

In China, employers really wont care how well you do your jobs as long as you're social. And if your guanxi is over 9000 you get the local government officials let you use an entire city as your own IRL game of GTA. Check out Li Gang/General Li is my daddy and remember the death sentence is routinely used for people who commit similar crimes, as the Chinese-language papers report every day.

You make connections in basically the same way as back home. Be extroverted, have lots of rich drinkin buddies, don't waste time on people who are significantly lower status than yourself. That part is the same.

I have found that all you need to do is to do what you would for friends or friends of friends in your own country. Treat them fairly, help them out, give them advice or answer questions if you can. I have now befriended a wide range of locals during my visits. I first met them because they were friends of my partner. Within that group are business people, a judge, regular working people, an employee at the airport who looks after VIP's etc. I also have to visit and have dinner with another varying group when I return in May because they all have asked me after I helped them out with some purchases of Australian products(at the normal price rather that the double or more that they were being charged by the rip off stores their tour guide was taking them to)  and took a few of them around to some places in Sydney when they were on a tour here last year.

So I would not do anything fake or special and if you are a decent person favours will be returned.

Though the so called "guanxi" built by all means may give us some help in some conditions,as Chinese,we all know it is not reliable when we are really in need ,especially if we have no money and influence.We may have lots of friends everywhere,but the ones we really cherish are just two or three.These people are the ones we see as our families.We would be honest to them and  would do whatever we could to help them out if they are in difficulty.Generally,Chinese are quite patient in finding themselves these close friends,the friendship is built little by little in years or even tens of years.

I'd tell you, but what are you gonna do for me?

By far, the thing that works best, without fail, for me is teaching the kid of some "important guy". We all meet lots of people here and whether they say it or not, their kids are the most important thing in their lives. If you can improve the kids prospects by helping with their English skill, the world is yours my friend.

Marry a woman who has tremedous guanxi, and it will become yours, also. Then, treat her like a Princess, and you are set.