Don't buy it for lettuce - fertilizer only speeds up grow of crops, it's does not affect quality or anything. Lettuce grows in 5 days no matter what.
It's for crops that say "mature in 5-8 days" you would need fertiizer to get more harvests. It's useful for something like cabbage and strawberries, or honeydews; not for lettuce or tea leaves.
If you just starting out, it's expensive, too, but later on it's OK - especially considering if you ship a lot of crops in season you get free fertilizer according to your farming degree.
As far how to apply it - I know someone said they only apply certain squares to save money, but that does not work for me, since week later other squares go down in ranks and crops do not mature evenly. I prefer just use happy fertilizer twice a month on field there I grow crops that need to be fertilized.