Learn Russian: Я покупаю сувенир.

In Russian, there is only one present tense. The verb покупаю can mean either "I buy" (in general) or "I am buying" (right now). The context tells you which one makes sense.

Since the souvenir is the object being bought, shouldn't it be in the accusative case? Why didn't the ending change?

It is in the accusative case! For masculine nouns that are inanimate (things, not people or animals), the accusative case looks exactly the same as the dictionary form. So сувенир doesn't change its ending here.

Why does the verb end in -ю?

The dictionary form of the verb is покупать (to buy). To match the pronoun я (I), you drop the -ть and add -ю. This is the standard pattern for most verbs ending in -ать.

Where is the word for "a" in this sentence?

Russian does not use articles like "a", "an", or "the". The word сувенир can translate to "a souvenir" or "the souvenir" depending on the situation.