Learn Russian: Анна сейчас встречает гостя.

In this sentence, the guest is the direct object receiving the action of being met, so we use the Accusative case. Because a guest is a living person (animate), masculine nouns change their ending rather than staying the same as they do for inanimate objects. Here, the base word гость changes to гостя.

Why is the ending for гостя an -я instead of an -а?

The dictionary form of the word is гость, which ends in a soft sign (-ь). When making a masculine animate noun Accusative, words ending in a standard hard consonant add -а (like студент becoming студента). But for words ending in a soft sign, we drop the sign and add the soft vowel -я.

Russian doesn't have an 'is doing' tense. How do we know it means 'is meeting' and not just 'meets'?

You are right that Russian uses the same present tense verb, встречает, for both 'meets' and 'is meeting'. The word сейчас means 'now', which tells us the action is happening at this very moment.

Could we put сейчас at the end of the sentence?

Yes, Russian word order is quite flexible. Анна встречает гостя сейчас is perfectly understandable. However, putting adverbs of time like сейчас before the verb is the most natural and common way to phrase it in Russian.