Yes, prettily is a word, an adverb meaning in a pretty way. Use it when you're describing how someone or something looks or acts in a pleasing manner: The table was prettily set with candles.
When prettily fits what you're writing
Describing a thing that looks charming as a result: The picture is painted very prettily. Your wording tells the reader the painting's appeal comes from how it was done, not just what it shows.
Describing how someone dressed or arranged something: She was prettily dressed for the garden party. This says the pleasing effect shows in the outfit itself, so use it when appearance is the point.
Describing manner or behavior: The children sang prettily at the recital. Here you're saying the performance had a pleasing quality, which works when you want a slightly old-fashioned, gentle tone.
Watch the linking verb. When look means seems, it takes an adjective, not the adverb: The garden looked pretty after the rain is right, and The garden looked prettily isn't. Prettily fits once an action appears, as in The beds were arranged prettily.
If your sentence needs a neutral or everyday tone, nicely may fit better; prettily carries a light, somewhat literary flavor, so it suits descriptions of appearance or graceful action rather than plain statements of fact.
For comparing two things you'll need the comparative form instead; see the prettier guidance in the next section.
Choosing between prettily and prettier
Describing an action done in a pleasing way? Then prettily fits: The napkins were folded prettily. Your wording tells the reader the charm lies in how the folding was done.
Prettily modifies a verb and describes a pleasing or attractive manner, as in She was prettily dressed for the garden party. It works whenever appearance shows through an action.
After a linking verb, you want the adjective instead: The garden looks pretty, because looks there means seems. The garden looks prettily isn't right.
Comparing two things? Switch to prettier: This room is prettier than that one. This room is decorated prettily than that one doesn't work, since prettily can't form comparisons.