Guinea pigs are very social, their closest wild relatives live in groups consist of 4-30 animals. The largest communities contain more boars, each of them is surrounded by 6-8 sows. Sometimes there are submissive boars as well, they do not mate.

Under domesticated circumstances you shouldn't keep more than one male with sows, the result could be lethal.

Cavy societies are built on strict hierarchy, each individual has its own place. Their positions can change through time.

Since they are prey animals, they tend to get scared easily. To make sure they feel safe, you must provide hideouts for them. Each cavy is different, but in general they are affraid of people in the beginning. Earning their trust requires patience and perseverance. When you bring new cavies home, it is perfectly normal if they do not come out for days, they even eat only when they are not seen. If you are unlucky, it might take months til they start not to be affraid when you show up.
Most of them become much tamer after a few weeks, and if you keep taking care of them, they will get used to your presence. The quickest approach is to offer delicacies, try to use the healthy ones.

Although they can be very different, in general we can say that cavies aren't so seriously into handling. This is the main reason why we suggest not to buy them for little children. As a result of the domestication they almost stopped biting humans, but if they are hurt, they are not affraid to use their incisors.
If you want to make sure that your cavies really want to interact with you, set up situations where the animals can choose whether they want contact. For example by sitting amongst them in a run. 

Hierarchy and social behaviour

Each guinea pig community is strictly hierarchical. Even if they are only two, their group is led by the dominant cavy. This piglet can do whatever he or she wants. All the rest are in a lower position compare to the dominant animal, but each of them is either in a better or worse place compare to the others.
Boars are kept in pairs, while sows are in pairs or larger groups. The latter can be completed with a neutered male.

In a group when there's a tension between cavies, generally the dominant animal intervenes, however low-scale conflicts might not raise his or her attention. Good groups have very few problems, but sometimes it is unavoidable. Male cavies often try to aquire a better position as they reach adulthood, while sows can feel the same way whenever they ovulate. These tensions are generally solved easily without any physical force or maybe through a little chasing and mounting.
Dominant cavies can discipline others with a nod, they do not need to use force very often.
The potential frustration can be reduced by providing a stimulating, interesting and large environment for them to live.

In case there is a fight, follow the events and make sure no physical harm is done. Sows basically never hurt each other seriously, but some bites can occur. Boars can be more rough, especially when the fight is about sows.
If the fight is quick, causes no harm, and the winner does not bully the submissive one unnecessarily, you can be relaxed. If someone is hurt, you must separate the piglets.

Certain situation can cause a change in the group dynamics. Pregnancies, new animals or sickness too. Make sure to check the health of the dominant animal in case he or she loses the leading position. Also, if a hitherto docile sow starts to act bullying and very dominant, investigate it too, it is often the sign of ovaryan cysts.

If you want well socialized cavies, keep them in groups.