Chances are this will be the shortest lesson. Adverbs are descriptive words for verbs. In English, most adverbs (but not all) end in -ly, such as quickly, angrily, etc. Spanish works in much the same way, except for that most of their verbs end in -mente. The only three common irregular adverbs in Spanish are bien (well), nunca, and jámas (both refer to the adverb never in English).
To convert a Spanish adjective into an adverb, all you need to do is change the adjective into its feminine form and add -mente to the end of it. For example:
malamente means badly.
rápidamente means quickly or rapidly.
lentamente means slowly.
As for the syntax, the English and Spanish syntaxes are the same. In a sentence:
Yo como decscuidadamente. I eat sloppily.
Yo corro rápidamente. I run quickly.