[v5 stem] + う / く / ぐ / す / つ / ぬ / ぶ / む / る [v1 stem] + る する 来る
The plain non-past, also called the dictionary form, is the form a verb has in the dictionary. At the end of a casual sentence it says what you do as a habit, what is generally true, or what you will do. Where polite speech has ます, casual speech has this form.
Verbs fall into three groups by how they end. A う-verb ends in one of the う-row sounds; a る-verb ends in る with an い- or え-row sound in front; する and くる来る are irregular.
An action verb in the non-past is never "I am doing it right now". 食べる is "I eat" or "I'll eat"; "I'm eating" is たべている食べている.
Verbs of state – ある, いる, わかる分かる, できる – are the exception: their non-past is the plain present. にほんご日本語がわかる分かる。 is "I understand Japanese".
A う-verb moves its last sound to the あ-row and adds ない; a verb in う takes わ. A る-verb drops る and adds ない. する becomes しない and 来る becomes こない来ない, read こない.
Many patterns take the dictionary form even when the sentence ends politely: とおもう思う, ことができる, まえに前に. Before 前に it stays non-past even when the whole sentence is about the past.