The best time to fertilize your trees is either early spring or late fall. Start with a soil test, available from your local tree or landscape service, or through your County Agricultural Extension Office. The soil test will tell you if the soil pH is in the proper range for your trees as well as if any nutrients are deficient.
The Primary Macronutrient Elements
The primary macronutrients, nitrogen (N), phosphorus (P), and potassium (K), are used by plants in the largest amounts and are the most likely to be deficient, especially nitrogen. Slow-release sources of nitrogen are preferable to highly soluble forms, which can burn plants if applied improperly. My personal preference is to fertilize my trees using good old-fashioned composted cow manure whenever it is practical. Use fertilizers containing phosphorus with care near waterways as it can cause runaway algal growth. This large mass of algae later depletes oxygen levels as it decomposes and this resulting diminished oxygen saturation of the water can kill fish and other aquatic organisms.
Note that, technically speaking, carbon (C), oxygen (O), and hydrogen (H) are considered macronutrients as well, and actually make up approximately 96% of the dry weight of a plant, however, since plants extract carbon and oxygen from the carbon dioxide (CO2) in the air, and hydrogen from the water (H2O) in the soil, these elements are commonly left out of the plant nutrient conversation.
The Secondary Macronutrient Elements
The secondary macronutrients, calcium, sulfur, and magnesium, are also used by plants in relatively large amounts. Calcium may not be present at optimum levels in your soil and can be supplemented by the addition of gypsum or lime. Be aware when using lime to supply calcium that it will tend to raise soil pH and most trees require a slightly acidic soil environment. Dolomitic lime adds magnesium in addition to calcium. Gypsum adds sulfur as well as calcium and does not change soil pH levels. The form of calcium found in gypsum is also much more water soluble than that in lime and is therefore more rapidly available to the plant, especially to deeper roots growing several inches below the soil surface. An additional benefit of using gypsum is that it helps improve soil structure by increasing porosity. In short, unless you are trying to raise your soil pH, I would recommend gypsum over lime for most tree fertilization situations.
The Micronutrient Elements
In addition to the macronutrients above, trees require a number of other elements in much smaller quantities. These are known as micronutrients and include iron, manganese, zinc, copper, boron, chlorine, and molybdenum. These elements and are usually present in sufficient quantities in the soil and rarely need to be supplemented.
Soil pH however affects the availability of micronutrients and plants can show symptoms of elemental deficiencies even when a soil test shows that there are adequate quantities present in the soil.
This is common in acid-loving plants such as those in the family Ericaceae, which includes rhododendrons, azaleas, pieris, mountain laurel, cranberries and blueberries. In neutral or alkaline soils (pH > 7) iron becomes less accessible and these plants will typically show yellowing between the leaf veins with the veins themselves remaining green, a symptom technically referred to as interveinal chlorosis.
An alkaline pH can cause a similar problem with manganese availability and causes similar symptoms. However, this is more commonly an issue in maples, dogwoods, and birch.
Note on Trees and Turf
If your trees are surrounded by turf, which is not recommended, much of any surface broadcast fertilizer is likely to be taken up by the grass before it can be absorbed by the tree roots. It is far better for the health of the tree to create a mulch bed extending out from the trunk as far as possible, ideally to the drip-line. This will give your tree a soil volume to grow in that is free from competition from grass roots for limited moisture, nutrient, and space resources.
If your trees are mulched you can easily pull back the mulch and use a rake to gently work some composted or dehydrated manure, or other organic compost, into the soil and then replace the mulch. A granular organic or slow-release chemical fertilizer could also be used. I recommend using chemical fertilizers in moderation, if at all, since many of the compounds used are chemical salts that can wreak havoc on the natural soil food web; the microorganisms and other life forms in the soil that are normally responsible for recycling soil nutrients and converting them into forms that can be absorbed by trees and other plants.
Mycorrhizal fungi, which form beneficial symbiotic relationships with the roots of virtually all species of trees, may also be harmed by chemical salts, as well as by certain pesticides. Many trees, especially mature trees, require this mycorrhizal association to be present and robust or tree health will suffer.
Lastly, and most importantly, remember that adding any fertilizer to your soil, beyond an annual application of quality compost, should be done only to address a specific nutrient deficiency or pH imbalance, and simply adding lime or fertilizer as a matter of course is often a waste of money that may potentially do more harm than good.