Learn Russian: Я найду десять ошибок в тексте.

Because of the number десять (ten). In Russian, quantities from 5 to 20, as well as any number ending in 5-9 or 0, require the following noun to be in the Genitive plural case. The Genitive plural of ошибка is ошибок.

Where does the -о- in ошибок come from? The dictionary form is ошибка.

To form the Genitive plural of most feminine nouns ending in -а, you normally just drop the -а. However, doing that to ошибка leaves ошибк, which ends in a clunky consonant cluster. To make it easier to pronounce, Russian inserts a "fill vowel" (usually о or е) between the final consonants, giving us ошибок.

найду means "I will find". Why isn't there a future tense helper word like буду?

найти (to find) is a perfective verb, meaning it focuses on the successful result or completion of an action. When you conjugate perfective verbs using the normal present-tense endings (я найду, ты найдёшь), they automatically form the future tense. You only use буду with imperfective verbs (like я буду искать — "I will be searching").

Why is it в тексте instead of в текст?