I'm sorry for your loss, and I'm afraid I haven't much to add, and that's despite having been in a similar position to yours twice.
ksandness has done a wonderful job covering the basics (and I can confirm
Q Shoe Guy's last post).
Many families won't welcome those from outside the family at the initial rites. The sympathy card and waiting for your cue from your colleagues seems the best thing you could have/can do.
But as you do feel close to the departed, if you choose to do so, I believe it would be appropriate to let the family know that you would like to pay your respects when you next go to Japan, even if this is outside the traditional mourning period. This will probably depend on the people involved, but for many families the deceased member stays as a vital presence in their lives and the household shrine can be a focus for ongoing communion and dialogue. If you are invited to their home to pay your respects (and even if you are not) you should bring an exquisitely wrapped or presented gift of food or candy, this gift (hopefully, something she enjoyed in life) will probably be placed on the alter so she can enjoy the essence - once the departed has had their share it will be eaten by the other family members.
You might be invited to light some incense for her, if so, you'll be shown where to put it.
Without clapping just bow your head and have a silent chat with her. When you are finished, bow again.
The same goes if you are invited instead to pay your respects at the grave.
But I'd suggest that it's best not to make the request if any of this would make you feel awkward. It's the kind of thing that would make everybody embarrassed unless your heart was in it.
There's a beautiful movie I'd recommend to you.
The Departed directed by Yojiro Takita.
In the coming years, the family may mark the anniversary at certain points. The first anniversary is a key event, and so is the 3rd and 7th anniversary (sometimes the 5th), there are other noted anniversaries after this (particularly the 13th) but they become less important. The priest may also set a day for memorial rites that doesn't coincide exactly with the anniversary date. You may like to mark these anniversaries on a calender. Again, depending on how close you were, some flowers or other token of acknowledgement appropriate for a shrine might be welcomed over the coming years.
The only tricky part is figuring out when these anniversaries are - the first will be next year, but the third may be the year after that (2012). The 7th anniversary is marked 6 years later (2016). It would be kind to respect these in regard to visits and company obligations.