There's another glacier, Tjøtabreen, that you can get a glimpse of when making the hike up to see the Briksdal Glacier and the 738 meter tall waterfall flowing from it unofficially named Tjøtafossen. You can only see a little part of the Tjøtabreen glacier unlike the Briksdal glacier which you can see quite a bit of.
There are couple of stunning photos of it on the World Waterfall Datatbase.
As you are hiking up to see the Briksdal glacier you will be walking alongside the water rushing out of the Kleivafossen waterfall and at some point you cross in front of it on the troll bridge. The source of the waterfall is the glacier itself. We got sprayed a little as we crossed, some reports say you get soaked, perhaps in the height of the summer when the glacier is melting faster. Resist the temptation to snap a lot of photos on the way up to the glacier if you want to try and beat the rest of the people on whatever tour or bus you come with, I really enjoyed the 1st 15 minutes or so when we were more or less up there by ourselves.
Briksdal glacier (Briksdalsbreen) is part of the Jostedalsbreen glacier, located in the Jostedalsbreen National Park. Once you get to it, the glacier and the national park are free to visit. From Olden where our cruise ship docked, it took about 45 minutes by bus to get to the welcome center, from there you have the option to hike to get a closer look at the glacier or take a troll car for a fee which gets you within about a 10 minute hike. We opted to hike the whole way, it took roughly 45 minutes each direction. The way up was a bit more work than the way down, if you are in reasonable shape you should be able to hike it.
You can't get right on top of the glacier, I'm guessing it could be rather dangerous to actually stand on the glacier as pieces of it break off from time to time. But you get pretty close, we were there almost by ourselves as we walk pretty fast, we saw part of the glacier break off, the crunching and crackling sound echoing through the area. Along the way you will see beautiful snow capped mountains, waterfalls and a glacial lake that feeds into one of the waterfalls.
If you take the public bus like we did, you should have about 2 1/2 to 3 hours to hike up, view the glacier and hike back down, plenty of time. Most of the other organized bus trips sounded like they gave you approximately the same amount of time.
Once at the glacier there were some rubber rafts you could rent to get closer to the glacier but I didn't really think it'd be worth a lot of extra money. It seems like you had to arrange for that at the welcome center, the guys we saw were likely waiting for cruise ship excursions as that was an option from ours.
The other major waterfall you'll see if you make the trip to Briksdal is the 300 meter tall Volefossen waterfall, you can see it for much of the walk up to the glacier from the visitor center.