One of my two Guinea Pigs died a couple of days ago.
I have heard from several sources that one pig on its own will suffer so I will get another. Should I do so immediately or wait a couple of weeks?
Sorry to hear that, my condolences on your loss. :(
Guinea pigs are definitely social animals (almost too social, it's how I ended up with 7 once before getting them sexed correctly), so being solo is going to be harder on your friend now than it would have been at a much earlier age. They do grieve, I think, based on my own experience with them, but the loss reaction isn't really that lengthy if there's a community with them, so I don't think there's a really easy rule of thumb there.
However, it's very easy to mistake signs of loneliness with signs of grief. Arguably, they're the same. So, I think you don't want to wait too long to bring some companionship back in, but you need to consider a couple of things:
The current home is this one's home first and (s)he has probably established some habits with respect to that.
The newcomer is coming into a whole new world with a whole new situation to contend with. That's a major stress.
You want to mitigate the above as much as possible. Ideally, what you want to do is have them in separate cages that are side-by-side. This is short term, so the newcomer could be in a smaller cage if necessary. In any event, the idea is to get them used to each other with some barrier to prevent any fights from happening as they become accustomed to each other's presence. Let this happen for a week or so.
After the initial "meeting" through the bars such that they're familiar and used to each other's scent, then look to introduce them in a less confined space. Do that for a few minutes at a time, to start, and gradually increase. Be prepared to break up a fight (be very careful doing that), but you need to allow them to establish a pecking order. Again, do this for a week or so.
Finally, once you're satisfied that they won't fight, you can house them together. This entire process will give your original pig a chance to grieve because the private space is still there while giving them a chance to get acquainted with a new friend.
I'm sorry for your loss.
Timing the introduction of a new pig depends on how much your current guinea pig is grieving. Observe the pig's mood and eating habits (weigh it daily to check for weight changes). Once your pig is no longer grieving, you should be able to introduce a new companion.
If your pig is grieving, you can try giving him a stuffed toy (make sure there's no parts that he could chew off) to cuddle with, or rearrange his cage or feeding/play schedule to make the loss seem more distant.
I'm so sorry for your loss, I know that she will stay in your heart forever. C: I would recommend to wait until you are ready to get another guinea pig. Your other piggy may feel sad for at least 1 month. She will sleep where the other piggy has slept, and may even yawn mournfully. It is sad to see, but I think you may want to wait until you think that you are ready, and your other piggy. I guess it all depends stability. I hope you feel better!