Here is a starting point. French verbs are classified in groups.

For the present tense, the first group (like manger, the majority of verbs belong to it) is using these endings:
-e (je)
-es (tu)
-e (il/elle/on)
-ons (nous)
-ez (vous)
-ent (ils/elles)

and all the other groups are often using these ones for the singular:
-s (je)
-s (tu)
-t (il/elle/on)
and often the same ones for the plural, but there are many irregular cases too.

Note that you eat might translate to either tu manges or vous mangez depending to who you talk to.

You do need to remember the endings for each person, but you don’t need to learn them separately for each verb and tense. For all tenses and for all verbs, the endings can only be in a small list:

• je → -e if the tu form ends in -es, -ai in a few cases (future, simple past, avoir → j’ai), otherwise -s
• tu → -s (possibly as part of -es)
• il/elle → -e if the tu form ends in -es¹, -a in a few cases (future, simple past, avoir → il a, aller → il va, otherwise -t (including être → il est) (except a handful of irregular verbs where there is -d or c with no additional -t)
• nous → -ons, except for a few irregular verbs and less common tenses that have -mes
• vous → -ez, except for a few irregular verbs and less common tenses that have -tes
• ils/elles → -ent or -ont (pronounced as if the nt part wasn’t there)

What goes before this suffix varies depending on the verb and the tense. It is not always the case that you can take a radical and add one of the suffixes above: sometimes the radical changes depending on the person. French conjugations are complicated and there are many irregular verbs. But the endings will always fall into the relatively few buckets above.

When the radical changes, this usually follows one of a few patterns for the singular forms and the third person plural:

• “je …e, tu …es, il/elle …e, ils/elles …ent”
• “je …ai, tu …as, il/elle …a, ils/elles …ont” (but first group simple past “ils/elles -èrent”)
• “je …s, tu …s, il/elle …t, ils/elles …ent” (but here there is often a difference between the singular forms and the third person plural, with a radical ending in a consonant that is modified differently depending on whether the ending starts with a consonant or a vowel; usually in those cases the third person plural is aligned with the first and second person plural)

For the first and second person plural, they almost always have the same radical modification (which may be different from the other persons) and then either “nous …ons, vous …ez” or “nous …mes, vous …tes”, but there are a few exceptions (e.g. être → nous sommes, vous êtes; dire → nous disons, vous dites).

¹ _{Not for the subjunctive imperfect, but if you know the subjunctive imperfect, that puts you above most French natives.}