Correct spelling, explanation: to create an adverb we usually add the suffix -ly to an adjective. In this case, the adjective is complete. As l in -ly is a consonant, there is no need to skip the e at the end (it is usually skipped when we glue some suffix beginning with I, for example completing). Therefore the correct spelling is completely. Spellings like completly are incorrect.

Definition of completely:
adverb, done in a complete matter, fully
This device broke and is completely useless right now.
I’m not completely sure if I want to go to the party tomorrow.

Incorrect spelling, explanation: completly is an incorrect form, because it comes from the adjective complete. To create an adverb we add the suffix -ly to the end of the word, so the correct form should be completely. There is no reason to skip e, so completely is the correct spelling.