Learn Spanish (Latin America): Pela la zanahoria con el cuchillo.

To give a direct command to someone you address as tú (informal 'you'), you use the affirmative imperative form. For regular verbs, you just drop the final s from the normal 'you' form. So, instead of tú pelas (you peel), the command is just pela (peel!). This makes it look exactly like the él/ella (he/she) present tense form.

How would I say this if I were speaking formally to someone using usted?

For regular verbs ending in -ar like pelar, the formal usted command swaps the usual vowel to an -e. So you would say pele la zanahoria con el cuchillo.

How do I pronounce the 'h' in the middle of zanahoria?

The h in Spanish is always silent, even in the middle of a word. You pronounce zanahoria smoothly as if the 'h' were not there at all, blending the vowels together.

Does con el combine into a single word the way del and al do?