Oh boy, this is tricky - I think the tricky part is is that you're asking a lot of good questions! I'll delve in to this with a primary focus on Egypt, with a slight focus on Howard Carter and a big one on his accompanying photographer, so I think I might unfortunately miss the daguerreotype period, but I will hit plate photography none-the-less!

How was photography used?

Well, by God, it was used for all sorts of things! On an Archaeological expedition it's (To the best of my knowledge) common practice to sketch items such as pottery, and with the advent of photography it became a lot easier to photograph artifacts along with a sketch, and it's a lot easier having a photograph, rather than a sketch, of the artifact to show to the community - doubly so for research when you don't have access to the object itself anymore, for whatever reason; It's a lot easier showing off complex writing, like this photograph by two Greek photographers in the late 19th century. One very interesting use for photography, and a very poignant one, was the opening of King Tut's tomb by Howard Carter. Most of the expedition was photographed by a man named Harry Burton who was, not only an Egyptologist, but also an archaeological photographer, an actual job! Burton had some 140 images published in Life magazine of a total of 1,400 taken together with Carter. He's quite a good example of what you might be looking for. Burton can be seen in the center, with Carter on the right, in this photograph taken in the 20s

With focus on the photograph of the unopened tomb, one can see why Harry Burton was such an attractive choice for this excavaction. He had trained extensively in Europe with some accompanying fame, and had even learned lighting techniques from Hollywood in order to further the quality of his images. Burton really captured the fleeting moment of being in front of that tomb, unopened for over three millennium, and I absolutely love going through his images. What's even better is that he took over 10,000 images, on top of hours of film footage.

Was the use purely documentary or were there attempts to make fine art photographs?

I would say there wasn't really many, to my knowledge, fine art photographs, at least not from the actual archaeological photographers. Burton did use some lighting techniques to 'enhance' the image and make it a little bit more pleasing, but I don't think he intended to create art, he was there to document the opening of the tomb, (and he continued to do so even after Carter's departure) but his photographs can be considered art in and of themselves in the way they were captured. Although one can certainly make the argument, with Burton's brilliant career in photographing art back in Italy, that he was more suited for the job of capturing the moment in which he was fortunate to have landed than someone else.

How were these photographs then used or disseminated in Europe?

The photographs were printed in newspapers and spread by this channel mainly. Here's one such example of early appearances of Burton's photographs in the papers.

Did photography replace sketch artists and lithographers on these explorations?

Not at all, they accompanied them! At least in the case of Harry Burton; Burton purchased a film camera in 1921 and used it (Without any formal teaching) in the same manner as his photographs, but they weren't really as widely circulated as his pictures for good reason - It's harder to distribute film evenly compared to re-printing photographic plates! The Metropolitan Museum of Art has actually done a massive exhibit on Harry Burton that I'd love to experience in person. There's a book as well that uses images from Burton that are also on display at the museum, called Tutankhamun's Tomb: The Thrill of Discovery: Photographs by Harry Burton which is definitely worth checking out. In my mind, I can still see how a lot of archaeologists would rather part way with strenuous and time-consuming painting and sketching of objects, and rather opt for a simple photograph, but sketches and etchings were still quite popular.

Look for some work by Sara Perry at York University (UK) - see here. Her dissertation is of interest to you. Her blogroll may have material of interest as well, might give you some leads.

This conference and the participants from Dan Hick's blog might give you some leads too.