The Imperative

Krystelle, 

it is just the case that some French verbs require a preposition following them sometimes or always - usually à or de, but other prepositions are needed sometimes.

It is a significant component of French grammar and language use to develop. 

There is no easy way to learn or predict which verbs require which prepositions - learning them in context is generally considered the best way in the long term. If you want to start looking at this area in depth, the links below are a good start.

Some verbs require a preposition before an infinitive verb. This is the case for ‘ essayer ‘ which takes the form ‘ essayer de ‘ when followed by an infinitive - in the exercise “ … essaie/essaye de le nettoyer toi-même. “

For the spelling - both forms you note are correct, for historical reasons, some verbs have more than 1 official correct spelling in certain conjugations.  (See last link)

https://kwiziq.learnfrenchwithalexa.com/learn/theme/3907147

 https://www.wordreference.com/fren/essayer

 https://www.lawlessfrench.com/grammar/verbs-with-de/

 https://www.lawlessfrench.com/grammar/verbs-with-a/

 https://www.lawlessfrench.com/grammar/a-vs-de-2/

 https://www.lawlessfrench.com/grammar/verbs-with-prepositions/ 

 Conjugate semi-regular -oyer/-ayer/-uyer verbs in the present tense in French (Le Présent)