Question
is it better to fertilize when the grass is dry, or is it okay when the grass is wet.


Answer
I recommend to fertilize the lawn when the grass blades are dry, and then water in immediately using plenty of water. This for several reasons.

Fertilizer applied to a dry lawn will fall through to the soil level and not stick to the leaves. This will result in a greater amount of fertilizer reaching the soil (where it is needed) and you avoid having fertilizer tied up for long times on the grass plants, and subject to damage from mowers, etc.

When fertilizer is surface applied, the urea (by far the most commonly used nitrogen source in commercial lawn fertilizers) has a tend to disapate in to the atmosphere due to reaction with dry soil thereby reducing the amount of active ingrediences being available for the lawn.

To get best result from your money, and to protect the health of the grass, always apply fertilizers to a dry lawn and then water in immediately with plenty of water.

The only exception is weed-and-feed products (fertilizer w/broadleaf weed control products mixed together). They must be applied to a wet lawn as the granulles must stick to the weed (and grass) leaves to be effective. I do not prefer these products for this very reason (they stick to grass leaves) and broadcasting weed control instead of spot spraying is not the best either. Therefore I generally do not recommend "weed-and-feed" products. Instead I fertilize seperately and spray for weeds seperately (e.g. using Weed-Be-Gon in a sprayer for example).

Note: when I say dry lawn, I mean that the grass blades are dry. The lawn should not be draught stressed. Usually watering deeply 2-3 days before applying will keep the lawn hydrated and healthy but has given the grass blades a chance to dry off.