Learn Russian: Я хотела бы попробовать этот десерт.

To make polite requests with "would like," Russian uses the conditional mood. You form this by taking the past tense of the verb—in this case, хотела (wanted)—and adding the particle бы. Even though it uses a past tense word, it expresses a present or future polite desire.

How do I know if I should use хотел бы or хотела бы?

The verb in a conditional phrase acts just like a regular past tense verb, meaning it must match the gender of the person speaking. Because the speaker here says Я хотела, we know she is female. A male speaker would say Я хотел бы.

Why does the sentence use the perfective verb попробовать instead of the imperfective пробовать?

You generally use a perfective verb when talking about a single, completed action with a result. Here, you want to taste the dessert one specific time to see if it's good, so the perfective попробовать is the most natural choice.

What case is этот десерт in, and why didn't the endings change?

It is in the accusative case because it is the direct object (the thing being tried). However, десерт is a masculine inanimate noun (a non-living thing). For masculine inanimate nouns, the accusative case looks exactly like the nominative (dictionary) form, which is why neither этот nor десерт change their endings here.