Flight

It's easy to book the flights yourself online. If you have a tour booked in Europe it's probably a good thing to arrive at least a day before to give you a bit of margin and some time to get over jetlag.

I'd arrive two days before the tour, because of the post- COVID airline chaos, with delayed and canceled flights.
Ask your tour to recommend a Venice hotel. Is this a cruise or a land tour? If a cruise, you may not be leaving from Venice proper, so get more details.
Flights are expensive this year. Check Google Flights to track prices and options. Always purchase flights directly from the airlines, do not use third party vendors.
Good luck!

Go to Google Flights
Search for a multi city flight
In to Venice
Out of Rome
Add days as you like before and after the tour dates
You will want to arrive at least by 9/10
So fly from LAX on 9/9

Book with the actual airlines
No third party

Search booking.com for hotels
Availability is limited-do this ASAP

No need for a travel agent

No need for a travel agent. Use a search engine (I like kayak) to find your flights. You want to select multi-city - from LAX to Venice and add a line for Rome to LAX. You should leave at least two days before your tour starts, so Sept 9. You will arrive on Sep 10. When you find a flight you like, go directly to the airline's website to book. This will save you headaches if there are changes in the flight, etc. because the airline will contact you directly rather than through a third party. Rick Steves tours provides the first hotel in registration information. See if you can book at the same hotel as the tour-go directly to the hotel website. If there doesn't appear to be availability, send them an e-mail which you can usually find on their website under Contact Info and tell them you are coming on a tour. If they don't have a room, ask them if they can recommend somewhere nearby. If you do have to go to another hotel, you can always check out and take your bags directly to the tour hotel where they will hold them until check in. I did a quick check and you will find good flights on major airlines with a base of under $1000 which is a good deal. Safe travels.

There are no direct flights to Venice from LAX
Be sure you pick one that gives you plenty of time to change planes

Is this a Rick Steves tour?

I agree that you might try Kayak first. Rick Steve’s recommends using Kayak and it certainly is a beginning point. Good luck!

Is this you as well, or just an odd coincidence?
https://community.ricksteves.com/travel-forum/general-europe/venice-florence-and-rome-travel-date-s-sept-11-20

If you want to keep it simple, ITA has direct nonstop flights between LAX and Rome. It is $1406 RT for Economy Classic on your dates. The plane arrives in Rome at noon. You could travel to Venice by train that day, or overnight in Rome near the train station and travel to Venice the next day.

ITA [cited above as UTA] also offers a connecting flight to Venice from FCO, but the layover is rather short. They have a later flight to Venice that they could put you on if you miss the connection - they would be responsible for getting you to Venice.

The advantage of ITA is that they have the nonstop from Rome to LAX for the return. Note that it doesn't operate every day. You might try calling them at their US number.

If you've never flown to Europe, a travel agent may not be a bad idea. While it's "easy" to search for flights online, it's also easy to make a bad choice if you don't know to look for things like adequate connection times, avoiding basic economy if you aren't willing to accept the restrictions, whether you need to pay extra for advance seat selection, etc. Kayak can be treacherous for newbies since they link to questionable third parties.

You should depart by Sept 9 at the latest.