How to correctly and accurately identify a few species of trees from their leaves?
A good first step is to pay attention to common differences between tree structure:

1. Alternate vs. Opposite structure


MADHORSE = your common eastern US opposite-leaved trees are Maple, Ash, Dogwood, and Horsechestnut (AKA buckeye).


2. Simple vs. compound leaves



3. Toothed ("entire") vs. untoothed leaves



4. Lobed vs. unlobed leaves



5. Differences in texture, hairiness, &amp; color of leaves


both b/w species and b/w top/bottom of leaves of the same species




Generally when you come across a new tree in Eastern N. America I'd recommend going through these steps: 


Is it alternate or opposite?
Is it simple or compound?
Is it toothed, doubly-toothed, or smooth along the edge?


If you can answer yes to (any or all of) those questions you typically SIGNIFICANTLY reduce your options. 

You also want to make sure you're aware of large variations in some species (especially oaks and hickories). One good example is the difference in shape, texture, and color of sun leaves vs. shade leaves of many species. 

Importantly, paying attention to WHERE the tree is located (and what else is growing around it) as this can really help narrow your choices. You'll also start recognizing common cohabitants of certain regions.  

Finally, don't be afraid to use your many senses (smelling, feeling and even tasting) -- though get to know poison ivy well before you start licking plants!!



Ok, now for some useful hints:


Red Oak = stereotypical oak shape, smooth on both side of leaf, lobes are not deep. You'll find 'spikes' at the end of each lobe. Bark looks like it has vertical shiny stripes.  
White Oak = rounded SMOOTH lobes. Bark light grey/white with flaking appearance when mature
Red Maple = OPPOSITE. Leaves serrated (toothed). Smooth grey bark (with few low-hanging branches)
Sugar Maple = OPPOSITE. Leaves NOT serrated. Smooth whiter grey bark.
Striped Maple = OPPOSITE. Maple-like shape, but with rounded/butt-shaped (cordate) base. Bark = very striped in appearance.
Tulip Poplar = Leaf-shape looks like a tulip flower. Tree tall and straight.
Black Cherry = Oval/round leaves with fine single-toothing along edge. Tuft of brown/white fur along mid-rib on underside of leaf. Bark = horizontal striping due to lenticels; gets flaky when mature. Bark/twigs have strong bad smell when scratched (cyanide).
White Pine = 5 relatively long wispy needles per cluster.
Virginia Pine = 3 Short, dense needles per cluster.  Bark has cornflake appearance. 
Dogwood = OPPOSITE. round leaf with deep ribbing veins and drip tip. Leaves often look to be growing in pairs. If you pull a leaf apart carefully, you'll find some thin tissues dangling between the halves. The bark is cobblestone (mosaic bumpy) and the shape of the tree is typically flat-umbrella-esque. 
Hickory Species = VERY DIFFICULT TO TELL SPECIES APART (though I can give you a bunch of hints to help). Fairly easy to tell apart from other species, though. Is ALTERNATE + COMPOUND with generally 5-9 leaflets per leaf. (unlike ash = opposite/compound or walnut = compound with MANY leaflets). Leaves often carry some odor and large seeds can be found nearby
Sourwood = Long, oval, tiny-toothed leaves that have strong sunken midrib and thin leaf texture. Tastes very sour. Bark is dark and ridged, and trunks very rarely grow straight (so look for crooked or leaning trees!).
Cucumber Magnolia = Look for LARGE, strongly veined leaves that are often drooping. Look for circular ring (stipule scar) beneath leaf petiole base.