Step 1 is getting to Rome.
Once here, you can take public transit, walk or taxi. The two nearest metro stops are Ottavino and Cipro, both located on the orange A line. From there it’s about a five minute walk.
You can take the #64 bus from Roma Termini (the main train station) or the #81 from the Colosseum.
Taxis are usually up to €20 from the historical center but if the weather is nice my favorite option is to walk. There is so much to take in when you’re in Rome and walking around is the best way to see it. Stop for espresso, pastries, an Aperol Spritz, gelato and a Roman pizza slice along the way.
Vatican City Museum Official Website for tickets, info and changes to regular hours and procedures to do Covid.
I wouldn’t recommend eating in Vatican City. It will be expensive and geared toward tourists. Head back to Rome to find the best spots to eat.