Don't believe it's lacquered or it wouldn't be so tarnished. Bar Keepers Friend will be the easiest and cheapest product to use. And you may need to use some Four Ought steel wool on those reddish spots. if you want a lovely finish, finish up with some brasso on a soft cloth.

Is it marked on the back?

There are no markings on the back. Thanks for the suggestions. I'll try them and keep my fingers crossed it's as simple as that!

It really is....stand over the sink and wet it, sprinkle on barkeepers friend and scrub it up....rinse very well....and product left on the tray will hasten the retarnishing.
There are those who will tell you to leave it alone as that is natural "patina"...I say nonsense, its dirt, clean it off, it wasn't meant to look like that. Would you leave a piece of dirty grimy furniture dirty and grimy? not talking about removing the finish and replacing but just removing dirt.

I bow to your knowledge.....Thanks so much!!

On the subject of lacquer, I don't know about decorative items like your tray, but the lacquers on brass musical instruments were pretty delicate until the 50s-60s. If your tray has/had the old nitrocellulose lacquer, it could definitely be failing. It comes off really easily--too easily--in hot water. So if you think it might have some lacquer on it, a nice hot soak is worth trying. If it's the old cruddy stuff, it'll come off the rest of the way. If it's the new stuff (or there's no lacquer), it'll just be cleaner. :)

If you want it to stay shiny after polishing, you can wax it with pure carnauba wax. (The car stuff.) It's non-toxic and comes off easily with dish soap.

I have had good luck with the liquid form of bar keeper's friend on an old brass bucket that I need to clean every now and then. It's comes out shiny and beautiful.

BKF comes in liquid? I didn't know!!

Fori - great information, thanks so much.
Richard, thanks for the idea of the liquid version of Bar Keepers Friend. Hopefully these ideas will help the restoration of the tray and we will get to that point.

I wonder if the liquid is less abrasive. Hmm!

Fori, I'll try what I have on a small section on the back, and if it's too abrasive, I'll get the liquid. Thanks for the thought.

I have a collection of antique brass push up candle sticks....and use it on them...it's not too abrasive...I get a fine shine. Also have a couple of brass trays that I use it on...well "had" gave a couple to my kids. But the liquid has to be easier!

Ack....so bright i need sunglasses! Well done!!
I had a plain brass tray I used as a Drink tray...it was keyhole shaped and could hold a bottle and glasses or an ice bucket and glasses. And it was plain and shiny like yours, and every drop of water that wasnt immediately dried left a spot. And I got fussy! So the tray that was supposed to protect the counter needed to b protected!
What are you going to use it for?

That's funny about your drink tray! Don't know what we're going to use this tray for as of yet, it's so handsome, and has such a nice weight to it. We'll definitely incorporate it into the holiday decor next Christmas. It'll look great with greens and red berries, but between now and then - we will find a great place to prop it up and admire it until we decide how we want to use it. Thanks again!

Pretty!

Now, if you feel like you want to put your new muscles to work, you can get almost a mirror finish with Mother's Aluminum & Mag polish.

I'm exhausted just thinking about it. :)

So now i am looking at the dingy copper tray in my kitchen and the 2 tarnished brass trays propped up on the top shelf in the family room...oh and the silver tray....adn the silver candlesticks.
You shame me.

It's a fine line between guilt and inspiration.

I'm still only half-way through that silverplated/exposed brass cornet...it'll re-tarnish before I'm done! It's like painting the Golden Gate Bridge.

Never heard of Mother's Aluminum & Mag polish! What new rabbit hole are you sending me down??!!!

If you do not use a polish after cleaning within weeks if not sooner your work will be for nothing. That Turtle wax mentioned above or a wax made for whatever you are working on will keep it looking good for longer.

maifleur03, thanks for the information, I wasn't aware. This has been a wonderful educational experience!

You'd think my cars would look nicer with all the car grooming products I have.

I've heard good things about Renaissance Wax too. It's supposedly used in museums which makes it the upscale version of car wax. :P