Learn Danish: Du skal prøve at tale tydeligt. - You must try to speak clearly.

Tydeligt translates to "clearly". It is an adverb of manner, meaning it describes how an action is done. You create these adverbs by adding a -t to the adjective tydelig (clear). This makes it look identical to the neuter adjective form you learned earlier (like in et tydeligt svar - a clear answer).

Why is there an at before tale but not before prøve?

This sentence has a chain of three verbs. Skal (must) is a modal verb, and modal verbs take an infinitive verb without at (to). That gives us skal prøve (must try). However, prøve is a regular verb, so the next verb in the chain needs the infinitive marker at, giving us at tale (to speak).

Could skal mean "will" in this sentence instead of "must"?

While skal is often used to express the future tense ("will" or "is going to"), here it expresses an obligation or necessity ("must"). You will often have to rely on context to tell the difference between the two meanings.