At a minimum, needs fresh belts, oil, brake fluid.

Find out the service history belts and valves. Clean out all gas from tank and fresh fuel, new battery, change  oil and hope it starts.
Kiss your BL ass for the rest of your life.

And OP is an asshole for letting a gift sit for 2 years

You need to know that you have a cool brother in law.

I have an 03 multi dark 620 and it’s my favorite. The multi and the monster have a lot in common. The service books are almost identical. The full service with desmo is up to 1500 bucks and recommended every 7.5k miles. I push mine further and adjust belt tension so I service closer to 12.5. The bike rips so hard. You are going to love it.

I have this bike - bought used last year - and what you said is perfect. You can do all of this yourself. Don’t worry about the valve clearance until later depending on miles. But do the belts for sure. 
Good luck!

Also check if the fuel that was in it while standing still those years is e5.
E10 could make the coating on the inside of the tank losen up. That could clog up the fuel line. Happened to my monster which caused it to not start. Garage had to basically clean the inside of the fueltank etc.

Would add to look for oily residue on the front forks indicating a leaking fork seal. And general pitting isn’t unheard of on these and don’t really seem to cause an issue from what I’ve have seen.

I have one of these and found them to be an excellent ride.   

Here is a minimum list of things to do, but not in an order of importance:

Belt life is two years installed, so replace those   
Empty the tank and use fresh petrol as the lighter chemicals will evaporate. Metal or plastic tank ? They need E5 fuel in a plastic tank as the Ethanol makes them swell up unless internally coated.  
Bike on a stand, spark plugs out, in gear, spin the back wheel lots to get the oil around.   
Replace the tyres as they will have perished   
Replace brake and clutch fluids   
Check the battery — its prolly dead by now.   
Replace the air filter and it’s prolly a nest or mouldy.   
Replace the engine oil and filter.    
Overhaul the brake callipers as the pistons may have stuck.   
Check the shiny bits of the forks and shock for pitting and corrosion.   
Same with the chain and sprockets.

Looking at the picture, the bike is in good condition.

Not immediately comparable. But I had this exact same bike with an S2R 800 swapped into it. The most fun I've ever had on two wheels, perfect amount of torque, versus weight, versus size. 

&#x200B;

Enjoy!

Belts on the two valve Ducatis are safe to run for more than two years I change every three to four years on my 900ss and they still look new when I do. But if in doubt about their age change them.

Awesome bike; is it your first? Awesome first bike, awesome bike . 

What everyone else said (less the haters)

Make sure the rear wheel is tight. Check the sprockets and chain, they should be buttery smooth. Maybe look at replacing if they looking aged as a crispy chain and sprocket make a world of difference. If you are city riding and changing sprockets you could consider changing the ratio to give you even more umph down low or Vice versa for highway. 

Note: your turn signal arms are going to get kicked and break, some stick splints and black hockey tape will fix.

Don’t let your partner sit too far back as the back tip of the seat will crush the taillight.

That it's one of the best Duc bikes every produced, and to stay on top of belts and valves.

Never EVER insist when you push the tank up ; it will break the weld on the back of it

Yeah, a few people have said, replace the belts. They are cheap and easy. Everything after that is easy! Of all the bikes I have owned ( 40+ yrs) the Ducati evokes the most emotion and i will say the maintenance has a certain zen that you might enjoy.

Check the belts for cracks, fresh gas, see if it starts up! May take quite a few cranks. Just let it sit between cranking sessions to not burn the starter. Mine has sat for a year without issues but takes a while to turn over.

Good hand me down…Good brother in law you found 😉

Congrats! The Monster 620 Dark was my first Ducati. Started the addiction. Enjoy it!

That is the first bike I ever owned. :) So many good times. Congrats!

You can do every job by yourself on this bike and it will drive for ever.

if it's been sitting the belts probably need to be replaced; they tend to deform if stuck in one position too long.  make sure the crankcase breather hasn't cracked.  both things are do-able at home if you're the slightest bit handy.

&#x200B;

otherwise, change the fluids, change the tires, point and go.

Brakes stop. Gas goes. Dummies will turn in front of you. So downshift and brake when they do. And helmets save domes

Own one myself. Fuel pump might go on you. FYI common issue with multiple years of that platform.

Brother in law gave me this Monster dark 600. Been sitting for a couple years. What do I need to know?