The short answer is that, except for modal verbs, the third person singular in the simple present tense always ends in –s: she climbs, he runs, it rains, etc.
Now for a more detailed answer: For the vast majority of verbs, the third person singular in the simple present is formed by adding –s to the main form. However there are a few spelling rules and irregular verbs to be aware of.
Spelling rules
Add –es instead of –s if the base form ends in -s, -z, -x, -sh, -ch, or the vowel o (but not -oo). This adds an extra syllable to the word in spoken form.
If the base form ends in consonant + y, remove the -y and add –ies:
Irregular verbs
Two very common irregular verbs that you already know do not follow the rules above (although their third person singular present forms do actually end in –s):
Modals
Finally, as mentioned above, the modal verbs, such as can, must, should, may and might, do not take -s in the third person singular present because, as you probably know, modal verbs do not take endings at all.