Opposite trees have buds growing in pairs on opposite sides of the twig. Alternate buds occur first on one side of the twig, the next one down on the other side of the twig, and so on, alternating sides. “Whorled” means more than two buds at the same level, the pattern of most conifers, which are covered in Pines, Evergreens, Conifers. The following description applies to broad-leaved deciduous trees. Shrubs (plants with multiple woody stems or trunks), which are frequently opposite, are not included here.
The leaves that emerge from the buds and the twigs that form also occur in the same pattern. If you can reach the buds or leaves on the lowest branches of the tree, it will be easy to determine whether the tree is opposite or alternate. Otherwise, you will have to gaze upward and check the twigs or leaves. Don’t forget that a twig, leaf, or branch can fall off, so check several sets in your appraisal.
Most deciduous trees are alternate, so if you discover a tree with opposite twigs and buds, you have considerably narrowed down the possibilities. Many field guides divide trees into opposite and alternate categories, so you know where to start looking. Because there are so few opposite trees, many regions have acronyms to help us remember them. Here in the Northeast, a popular one is MAD Dog, which stands for Maple, Ash, and Dogwood. Two trickster trees in this area are Catalpa, whose twigs occur in opposite pairs or in whorls of three, and Horse chestnut, which has opposite buds, but soon after the leaves emerge, one of each pair falls off. From the southern part of New York State southward, you may have to use the acronym DAMP, because there are two non-native species, Paulownia and Phellodendron, that sometimes occur.
Next, look at the size of the twigs. Ash trees have compound leaves, meaning that multiple leaflets are borne by a single, long leaf stem which falls off in the autumn. Ash leaves are pinnate, with the leaflets lining two sides of the leaf stem. The twigs that support compound leaves have to be stout and strong. Ash has a distinctive silhouette of thick, slightly curving twigs. White ash bark is furrowed, and buds are dry and scratchy. Horse chestnut also has thick twigs because it also has compound leaves, with leaflets in a palmate pattern, all arising from the end of the stem and spread out like fingers. Horse chestnut buds are large and sticky but have no discernible odor. Catalpa has heart-shaped, simple (i.e., not compound) leaves, but they are huge, so the twigs are fat.
Maple twigs are thin and graceful, with many small twigs branching off the larger ones. Red maples have roundish red buds, often clustered, and smooth or scaly grey bark. Sugar maples have pointed, brown buds, bumpy bark, and often a smooth, whitish lichen on the trunk. Leaves are the familiar squarish, lobed shape.
Dogwoods rarely grow over thirty feet and are usually found out in the open or in sparse, young woods where they can get sufficient sunlight. If your tree is tall or in deep woods, therefore, you can rule out dogwood. Flowering dogwood has onion-shaped buds. Just to be troublesome, there is one native dogwood with alternate leaves, known as alternate-leaved dogwood, with blue-black berries. The other dogwoods tend to be more shrubby, having many trunks from the same root system. Leaves are egg-shaped and pointed at both ends.
For more on tree ID terms, see "Identifying Features of Trees". For information on leaves, see Identifying Trees by Their Leaves.