Question
when is the best time to fertilize

Answer
Hi John,  When, how much and how often, depends on the type grass you are growing.  Here are the most common types, write me back if I've overlooked yours:
Bermuda - Every 30 days from late March/early April until last feeding in early September. 1 lb. of nitrogen per 1000 sq. ft. each feeding.
Zoysia  -  Every 60 days as above. Same amount of nitrogen.
St. Augustine and Centipede -  Every 45-60 days as above but 1/2 lb. of nitrogen per 1000 sq. ft. each feeding.
Fescue and Bluegrass  -  One feeding in March/April and another in late September or early October.  1/2 lb. of nitrogen per 1000. sq. ft.
For top quality turf...
Never use fertilizers with only ammoniacal nitrogen. Choose a good quality, slow release fertilizer.
The more you fertilize, the more often you need to mow.
Never remove more than 1/3 of the leaf blade at a time.
Keep your pH around 6 to 6.5.
Based on a soil test, you may want to substitute the last feeding of the year with a nitrogen free fertilizer such as 0-20-20.
Jim