You must befriend Martha and bring her wool. Two Hearts.

You must befriend Woody, Joe or Kurt. One Heart.

You must ship 30 Cabbages.

You must befriend the Mayor. One, two, three hearts.

When you have enough fishing experience to obtain a Copper Fishing Rod, you can get one free by simply walking to the Lake. You will experience a scene with Ray wherein he will give you a Professional Fisherman's 125 which is nothing more nor less than a Copper Fishing Rod. (When you see the Copper Fishing Rod at the Junk Shop, go to the Lake instead! You can find your experience level for all Tools in your Menu as well.)

When you want to make certain that you obtain the best product from your Sheep or Cow, save your game before you shear the Sheep or milk the cow. If you do not obtain the best product, reload your game without saving. The product is random and is loaded at the moment when you use the tool. A high heart level increases the odds of obtaining a superior product but the event is random.

When you have received 50 Musical Notes, go to the Goddess Spring. The Harvest Goddess will be restored to life and your reward will be that henceforth, each time you visit the Spring, your energy will be fully restored. (You will be treated to a false ending typical of Harvest Moon... the game continues.)

Rather than being subjected to the random cracks in the mines, you can use your hoe to find the stairs to the next floor. By running, you will be able to see a faint light on two sides of the square that conceals the stairway. You only will see it if you are in motion. Use your hoe to uncover the stairs. It usually but not always will be within three squares of the stairway that will return you to the ground floor.

Here is a list of how many hearts you have to have with the mayor and cost of different land you can buy

HEARTS   LOCATION                COST
  0      3-1 FLOWER BUD          5,000
  0      4 RIVER SONG HEIGHTS    5,000
  0      2 SEA BREEZE            5,000
  1      2 MOUNTAIN ECHO FOREST  7,000
  1      3 MOUNTAIN ECHO FOREST  7,000
  1      FLOWER BUD POINT        7,000
  1      1 SEA BREEZE            7,000
  2      3-2 FLOWER BUD          10,000
  2      4-3 FLOWER BUD          10,000
  2      1 RIVER SONG HEIGHTS    10,000
  2      1 MOUNTAIN ECHO FOREST  10,000
  2      1 WOODMAN'S FOREST      10,000

There are 8 other lands you can purchase that require the mayor to have 3 hearts they cost 15,000 except for the forest of fountains those cost 30,000.