The high score of each level is displayed in the upper right corner of the screen. You also know that you got a high score if you get a gold medal at the end of the level. Between levels you can back out of the world map and go a few steps left to see which medal you have in each level.
For the scoring, there are exactly three things you need to care about, in this order:
1. Fruits! Most levels have three fruits to collect and if you get them, you will get double score at the end of level. They are quite easy to find, but if you want to make it even easier, check the video at the end of the guide. Levels, which don't have the fruits are boss battles and flying levels, but the score is generally very easy to reach in these levels as well.
2. Scare tactics & eating ghosts. When you do the
action with regular Pac, the ghosts nearby will turn blue and you can get up to 3200 points from them. Spare this until you have at least 5 ghosts around you and eat them in rapid succession! You can recharge the power by eating 5 regular ghosts. Eat regular ghosts with Pac's special forms when available, because they give more points and possibly give progress to other cheevos as well.
3. Silver coins. There are coins around which give you score multiplier for a brief time. 1 coin = score x 2, 2 coins = score x 3 etc. If possible, pair these up with tip #2.
You also get a small amount of points from collecting items during the levels and an equally small amount of bonus points at the end of the level for collected Pac Pellets (the yellow orbs) and ghost eyes (ghosts eaten). I wouldn't give too much emphasis on these, as the points awarded are very small and the score limit is easy to reach once you learn how to use the Scare Tactics.
Here's a video displaying all the fruit locations in Space. I take no credit for the video.