Learn Russian: Мы видим талантливого актёра.

Because it is modifying the direct object of the sentence, актёра, so it must be in the Accusative case. Since актёр is a masculine animate noun (a living being), its adjectives take the special animate Accusative ending -ого instead of just keeping their Nominative form.

How is the -ого ending in талантливого pronounced?

The letter г in the masculine endings -ого and -его is always pronounced like an English v. Because the ending is unstressed here, the о sounds reduce, making the ending sound roughly like -ava.

Why does the noun актёра end in -а?

Because актёр is a masculine animate noun in the Accusative case. For animate masculine nouns, the Accusative case borrows the Genitive case ending, which means adding an -а. If the noun were inanimate (like a table, стол), it would not change at all.

Why does видим end in -им if its dictionary form видеть ends in -еть?

Usually, verbs ending in -еть belong to the first conjugation and take endings like -ем. However, видеть is one of a few common exception verbs that belong to the second conjugation, which is why it uses -им for the мы (we) form.