Eudicot leaves tend to have netted venation, with a larger central vein (the midrib or midvein) that branches off into a network of smaller veins. In the image below, you can see this branching pattern in a skeletal leaf.
Eudicot leaves can usually be distinguished by netted venation at the macroscopic level, but they also differ at the microscopic level. Note the difference in organization between the tissues in the leaf below and the leaves shown in the monocot section.
You will often see a waxy cuticle coating the surface of most plant tissues. In leaves, the location and thickness of the cuticle can give you clues about the environment that the plant has adapted to.
Seeing vascular bundles of eudicots in cross sections can be confusing. The organization of tissues in the much larger midrib vascular bundle is often spread out into a semicircle, still with xylem on the top and phloem on the bottom, but they can be difficult to distinguish. In addition to this, the smaller veins are not oriented in the same direction, as they are in monocots.
In the image below, the vascular bundle just to the left of the midrib is coming more or less straight at us, so it is easy to distinguish the tissues. In contrast, the vascular bundle to the right of the midrib was moving diagonally and so was caught in an oblique section and looks more like a smear. Often with these oblique sections, you can distinguish the xylem cells by their strange secondary wall thickenings -- they look a bit like coiled springs.