When you first begin the game, you won't be powerful enough to do much other than fight Tomators in the Tomato Patch, so don't leave the screen where you begin the game. You can always restore your health by examining the exact spot where the game starts.
After you gain a couple levels and learn Tomato Cure, you might want to move to the screen below you... there are Tomators and Cockadoodletwos there. You want to fight the Cockadoodletwos because they occasionally drop Cabbage Leaves, which is one of only two pieces of armor in the game, and you'll definitely want to pick it up.
If you're feeling really brave, you can make a mad dash to the barn, which is to the east. If you're not strong enough (and you won't be unless you spend some time leveling up), you can run from all the battles, and hope that you survive. When you make it to the barn, pick up the Pitchfork, which will increase your power, and pick up the Key, just beyond the exit. Then be sure to save your game. You can do this even at Level 1, if you're lucky, which can make levelling up a bit easier.
Once you get the Key, Pitchfork and Cabbage Leaves, you'll want to level up. Your next goal will be to fight Old Bessy, just south of the barn. You can only access her if you have the Key. You'll probably want to be at level 8 or 9 before you fight her. For boss battles, I'd just suggest pounding away, and using Tomato Cure when you need to. Super Power can help, but it also sucks up your MP pretty quickly, so I never use it. If you over-level, though, you can bypass this battle completely. At level 12, Tomato will pass harmlessly through Old Bessy, without needing to fight at all.
Once you defeat Old Bessy, you can access the second half of the map. To the east of the pond is the Silo, to the west is the graveyard, and to the south is Farmer Bob. The outhouse near the silo is another recovery spot, so it's a good place to level up. But first, you should head to the graveyard. In the upper-left corner, you'll find the Reaper, the best weapon in the game. Also, by fighting the Cownt Draculas here, you can win the Cow Hide, the best armor in the game. But nothing else is important at the graveyard (other than some tombstones that play music).
Not much you have to do now other than level up and take out Farmer Bob. You'll want to be around level 20 before you do so (if you're under level 20, you get a different ending than if you're at level 20 or over, so you may want to fight him at level 19 to start out with). Battle him with the same tactics as you used against Old Bessy, and with some luck, you'll emerge victorious. As for which ending you'll get, go ahead and consult the endings page.