I am writing this based on my experiences, including the crying mentioned above. Most of my frustration comes from not recognizing the features described in the next step of the key. Learning these features will save you a lot of time, frustration, and quite a few tissues. A sharp pocket knife and a small 10x magnifier will help too. The magnifier is helpful for looking at buds and a necessity for older eyes to count the bundle scars.
These two examples demonstrate some features you need to know. The picture on the left shows that the leaf scars below the bud are at different levels. This tells you that the leaves are alternate. You can even make out multiple vascular bundle scars (tiny white spots) in the leaf scar on the left side of this tulip tree twig. The key will ask you about the location of the leaf scar and the number of bundle scars. Notice the two scales fit tightly together in a straight line, called "valvate"in a key.On the right, the sugar maple has opposite buds and complex overlapping scales, referred to as "imbricate". Twig color, hairiness, and the shape and arrangement of the leaf scars are all important identifying features in a key.
The "key" to using a key is to know your twig anatomy. Every time I get lost, it is because I couldn't properly identify twig features in the next step. If you don't know a vascular bundle scar from a stipule, start by learning a few basic structures. A good place to start is this forestry.about.com diagram which will open in another window. Look it over and then come back here.
Now that you are back, open bobklips.com twig pictures. Bob writes from Columbus Ohio, an area with similar trees to Missouri's. (My New York friends think Ohio is the Midwest- actually it is just the eastern edge.) He has some vivid bud and twig pictures which will help you visualize what you saw in the diagrams above.
Now that you have seen Bob Klip's examples of bud arrangement, leaf scars and vascular bundles, you are ready to key in. I would suggest that you head outside and get a few twigs from trees whose identities are known to you. Sycamore, walnut and maples are good species to choose as their features are larger and you are more likely to find early success.
The knife mentioned above is used to get to the pith in the center of the twig. Most pith is just that, a soft homogenous material filling of the center as seen at the left in the Tree of Heaven (or Hell depending on your feelings about invasive plants). Some species such as the black walnut on the right have chambered pith, and a few other species are actually hollow.Now you may want to go to the Virginia Tech vTree Twig Key which will open in another window on your browser. Plunge in and enjoy. Oh, you might also have a box of tissues nearby if you fail your first attempts, but just keep on keying.
The Missouri Department of Conservation has A Key to Missouri Trees in Winter which you can buy at the Nature Center. It is handy to use in the field.
Virginia Tech has a vTree Android app which is helpful as a key with over 900 species fact sheets. It takes a long time to install but is well worth the wait.
Thanks to Bob Klips for the pictures. The emphasis is on plants with gorgeous detailed photographs on his bobklips.com website.