Answer: Usually, the best approach is to run some basic soil tests and find out what kind of fertility is already there, then fertilize (if needed) on the basis of the results. Your county extension should be able to help you with the results and interpreting the results.
In general, you can use an all-purpose granular fertilizer such as 10-10-10 on trees and shrubs. Read and follow the label instructions. If they are located in a lawn and you fertilize the lawn, then you probably would not need to fertilize the trees and shrubs separately.
Rhododendrons and azaleas do require an acid soil, so you might need to use a fertilizer (granular or a foliar liquid as you prefer) for acid loving plants if the pH of your soil is neutral or alkaline and thus the soil is not acid enough for them. (For the same reason, avoid applying lime in the root area of these shrubs.) The only way to know this for sure is to run those soil tests. Again, you would read and follow the label directions.
The best time to fertilize most evergreens is in the spring, but for most deciduous trees and shrubs the best time is in late fall right after the leaves drop. For deciduous trees and shrubs you can also split the applications between fall, very early spring and again in late spring. Do not overfertilize however, because you could burn the plants or encourage overly lush, weak growth. Too much fertilizer is not better than no fertilizer at all.
You may also want to use compost instead of or along with the fertilizer. Using several inches of organic mulch year round also helps to feed the soil as it breaks down.
Lastly, for newly planted things the most important thing you can do is make sure the soil stays evenly moist but not sopping wet while they are becoming established, typically three years or up to five years in severe drought conditions. Deep watering as needed (check the soil with your fingers) is better than a daily sprinkling, and using that mulch will help moderate the soil temperature, keep the soil moist and hold down weeds.
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