To expand, what tactics were used? Equipment? Did the Romans try to attack large towns in the region first? How did these assaults go and was the losses usually high? What paths did the Romans take for the invasion route?
Caesar's invasion of Britain (which he wrote about in the Gallic Wars) was a disaster. He set out late in the campaigning season, with almost no intelligence. He sent one ship to scout, but it didn't even make landing. The British blocked his first attempt to land, and second - Caesar says because he was not using shallow draft ships appropriate to the Mediterranean but instead deep-draft ships appropriate to ocean travel. The result was Caesar got as close as he could, and had his regular legionaries wade ashore against British opposition, and they did not like this idea and almost wouldn't do it.
Caesar's cavalry was coming across separately and got scattered across the channel by a storm. Caesar's own ships got caught in a storm and he lost a bunch of them - partly through ignorance of tides. Short on supplies he sent foragers, who got themselves ambushed; without a cavalry he had no good response for Celtic chariots, and ended up negotiating a peace and went home.
The next year he went back with more than twice as many soldiers (5 legions instead of 2 and 2000 horse); a better idea of where to find a suitable landing, better sailing conditions, and established a beach head easily enough. This time the skirmishing tactics of the Celts were not as effective. Caesar lost his fleet in a storm - again. While repairing his ships the two sides fell into a kind of stalemate; Britons couldn't get inside Caesar's fort, and Caesar couldn't pursue the skirmishers effectively. In the end, the British alliance collapsed because of politics, and Caesar needed to go back to Gaul to deal with a famine and revolt there, so they negotiated a peace and Caesar took off.
This is basically a summary of BG 4 and 5; I skipped a lot of the geography and ethnographic stuff. The Brits managed to confine Caesar as long as they only harassed foragers; Caesar needs to forage to feed his army. There were a couple of times Caesar managed to catch some of his enemies, when they came too near the fort for instance, but otherwise it didn't go well at all.
I don't know as much about Claudius' invasion. Simply by his success it must have gone better.