Then it is either fast running around or slowly and methodically scout out a small area and then try to eliminate all enemies in that area before moving on. The Swamps can be hard at first - you need to find your way to survive in them.
Another option would be to go to another Swamp area - some Swamps are "not good" to start in - i did that myself a few times as it is a better option than dying/failing all the time.
Also be aware of the fact that narrow strips of Swamp (mostly found as going from the north to the south) may not have Dungeons at all.