Learn French: Voici le candidat que nous élirons demain. - Here is the candidate that we will elect tomorrow.

The verb is élire (to elect), which is a regular -re verb. To form the futur simple, you drop the final e from the infinitive to get your stem (élir-). Then you add the future ending for nous, which is -ons, giving you nous élirons.

In English, we often say "the candidate we will elect" without using "that". Can we do that in French?

No, you can never drop que (that/whom) in French. You must always include it to connect the two parts of the sentence: le candidat que nous élirons.

I sometimes mix up qui and que. Why do we use que here?

You use que when the word it replaces is the object of the next verb. Here, nous (we) is the subject doing the electing, and the candidate is the object receiving the action. If the candidate were doing the action (for example, "the candidate who speaks"), you would use qui instead.

Could I use voilà instead of voici?