Seems easy enough, but it can get complicated. If a plant "has leaves" it means they're visible and they're, as far as you can tell, carrying out the leaf function of photosynthesis.
No leaves? Not as simple as it sounds. It could have no leaves, but instead have a petiole that evolved to look like a leaf and take over the leaf's job of photosynthesis. Those are called phyllodes.
The arrangement of leaves along the stem.
Alternate leaves alternate their way up the stem. Each leaf grows from it's own node. They can alternate side to side, spiral around the stem or be randomly scattered along the stem.
Two opposite leaves grow from the same node on the stem. but stick out in opposite directions.
Leaves are whorled if three or more of them grow out of a single node.
As simple leaf is, well simple. It's just a leaf. Undivided. To get how that differentiates plants, read on. There are unsimple leaves.
For instance palmate leaves. Instead of being simple, palmate leaves are compound: one leaf divided into separate leaflets. Palmate leaves have two or more leaflets growing from the same petiole. They look a bit like your hand, thus the name palmate.
Then there's pinnate. These definitely look like separate leaves, but they're not. They're one leaf made up of leaflets arranged along stem. The stem that connects pinnate leaves is called a rachis, and it extends from the petiole.
Pinnate leaves can be even pinnate or odd pinnate. Even pinnate leaves have an even number of leaflets. They're sometimes called paripinnate because the leaves are in pairs.
Odd pinnate leaves have an odd number of leaves arranged in two rows of pairs with a final leaf sticking out from the end of the rachis. Odd-pinnate leaves are sometimes called imparipinnate because compound leaves deserve absurdly-compound names.
Bipinnate leaves are pinnate leaves where each leaflet is divided pinnately. Another name for bipinnate is twice-pinnate to avoid having to say pinnately-pinnate.
There are more leaf arrangements. Lots more. Just Google "compound leaf types" to see how many.
Leaves come in a lot of different shapes. More than you can shake a stick at. The range of shape names can make describing leaves precise, but there's a problem. Leaves themselves aren't precise. The leaves of a single species can vary enough to cover more than one precise shape description. These are a few of the more general shapes.
Shaped like the point on a lance. Wider than it is long, tapering to a point at the apex.
Shaped like an egg, but flat. Wider at the base and narrower at the apex. Ovate leaves are wider and more rounded than Lanceolate leaves.
Linnear leaves are usually pretty narrow, but specifically much longer than they are wide.
Heart shaped. Kind of ovate, but with a deep notch at the base.
Shaped like a cucumber. Rounded base and apex with the sides roughly parallel.
You'd think it means shaped like a spatula, but spatulate leaves are really more spoon shaped.
The edges of a leaf are called the margin. And there's a variety of margin types.
An entire leave is entirely smooth all the way around.
Toothed around the edges, but not like your teeth. More like the teeth of a cartoon dragon.
Like dentate, but the "teeth" are more rounded.
Serrate leaves have teeth too, but they're small and tilted toward the apex.
Now the teeth on these leaves look a bit like your teeth. Like dentate and crenate, but kind of flat top with a notch cut into it.
The incisions in lobed leaves are farther apart and deeper than dentate, etc. The incisions can be up to half-way to the midrib.
Hairy leaves have little hairs on the top or the bottom.
Glabrous leaves don't have any hairs on the top or the bottom.
Measure a leaf blade from the base (not including the petiole) to the apex. Flatten out the leaf to get the full length. As soon as you measure a leaf you'll notice that other leaves on the plant aren't the same size. Measure a few leaves and go with the average, or the range. If the leaves are all exactly the same length, check to make sure it isn't a fake, plastic plant.
The veins in leaves have distinct patterns that are helpful in identifying the plant (and helpful to leaf function).
Check the top and the bottom, if you don't see any veins (or you think maybe you can make out what could be veins), call it no venation.
Only the midrib is clearly visible (secondary and tertiary venation are indiscernible).
The midrib has clearly-visible lateral veins branching off and running out to the margin.