The three forms you give are the simple present, the simple past and the past participle.
The simple present "eat" and simple past "ate" are used without another verb (Example) "I eat", "he ate".
Participles have to be used with another verb, called the auxiliary verb. For past participles, the auxiliary verb is "to have": "I have eaten", "Has he already eaten?" (perfect tense); "I had eaten", "Had he already eaten?" (pluperfect tense).
There is one last form of the verb, and that is the present participle, which ends in "-ing". This participle is used with the auxiliary verb "to be": "I am eating", "Was he eating