First, congrats on the new-to-you BX. You are going to enjoy that little tractor.
The levers on the right fender are high and low gear range, 4wd/2wd, and 3ph. Do not force the gear range lever or the 4wd lever. When you use 4wd, you will probably have to very slowly move the tractor forward and backward in a straight line while applying slight pressure to the lever to disengage. You will get the feel for it quickly, just don't force anything and don't use it any more than neccessary to save wear and tear on the driveline. If you have a 4th lever it will be for rear hydraulics. The left fender has the pto lever and the pto selecter (rear, both, and mid pto).
Below the seat is a seat adjustment lever (slides the seat forward and aft) and a knob for adjusting cutting height on the MMM. To adjust the knob, raise the 3ph lever (it also operates the MMM) to the top before trying to turn the knob. Don't trust the heights that are on the knob, they will be off so you will need to measure the distance from the ground to the blades to determine your actual cutting height and make a mental note of the knob setting.
The right foot has the forward-reverse pedal and above that is the brake pedal. The left foot has the parking brake lock (hold the brake and push the brake lock) and the differential lock (push and hold when needed). As 4Kings said, there is no clutch.
There are 3 switches on the dash, headlights, hazzards, and turn signals. These switches are not waterproof so don't panic when your lights go crazy when you get caught in the rain one day! They will dry out and be fine, just don't plan on storing your tractor outside in the weather. The battery is under the steering wheel behind the black screen.
The hood release is on the right side of the steering column. Under the hood, the air filter is on the top left side of the motor and the oil dipstick is on the right side. There is a trash screen that lifts out in front of the radiator just in front of the console. The front axle has a dip stick by the right front tire and the hydraulic dipstick is on the left side of the PTO. The hydraulic fill is right above the pto and you will need a flexable funnel to put fluid in. There is much discussion about using UDT or SUDT fluids, so you will have to make that decision for yourself.
The only grease fitting on your tractor is the hydro pedal. It gets one squirt of grease about every 50 hrs. You will have grease fittings on all 3 spindles of your MMM.
To start the tractor, lower the 3ph, hold the brake, put the transmission in neutral, make sure the pto is turned off (actually pull the lever), and open the throttle just a little. Turn the key until you see the glow plug light on the dash and hold it there for about 10 sec if the air temps are warm (longer in cold weather) then turn the key to start.
With only a MMM on the tractor, you will find that you want very little air in the tires. You will have to play with pressures to find what is comfortable.
You should check with a Kubota dealer and order an Owners Manual because it has a good bit of useful information, including operating capacities and maintenance schedules. I don't think they are very expensive, I think $20 or $25. It isn't something you'll reference every day, but it is very nice to have and it does tell you required fluids and quantities. There should also be a manual for the MMM available as well.
The MMM will operate at near full throttle. Full throttle is about 3200 rpm and the MMM is made for the tracor to run at about 3050 rpm. To start, open the trottle, choose the mid-pto on the lever, then engage the pto lever. To stop, just disengage the pto lever. You will normally mow in low gear.
If you can't find out the service history, definately change out the engine oil, hydraulic fluid, and filters. After that, engine oil is at every 100 hrs (and I change the filter, too) and new hydraulic fluid, filter and clean screen every 300 hrs.
That should be enough to get you started. Just play with it and get a feel for everything. Oh, and don't forget to use your seatbelt. Not only will it help keep you safe if you roll over, but it will help hold you in the seat when you go bouncing across the yard!