First, here's a link to a free download of your manual
. You should review it from time to time and consult it when you're stuck on a problem. The page numbers in my answer refer to this document.
The settings that impact overall image quality are:
1) ISO Sensitivity (Page 51). This is the sensitivity to light. A properly exposed picture taken at ISO 100 could be taken at ISO 400 in just 1/4 of the time. This means if the subject is blurry at ISO 100, you'll have a better chance of "freezing the action" if you shoot at ISO 400. Overall, the lower the value, the better the picture. Lower ISO values are ideal for bright, sunlit pictures. Higher values tend to be grainier, and are better suited for dark, overcast days and indoors under artificial light. I found shooting my DMC-ZS3 that ISO higher than 400 are too muddied for my liking - try the settings to see what is acceptable to you.
2) Picture Size (Page 52). Pictures that are set for 5M, 6M and 7M (5, 6 & 7 Megabytes respectively) contain a great deal more information than a picture taken of the exact same subject at 0.3M, 1M and 2M (300kb, 1 and 2 Megabytes respectively). A seven megabyte (7M) picture holds over 20 times more information than the 300kb (0.3M) picture of the same subject. This can be hard to detect on our small screens in the camera, but when viewed on a computer monitor, it starts to become noticeable - quickly. Viewing on a 17" computer screen is 8 times larger than the 2 inch screen of the camera - this is effectively "enlarging" the picture.
3) Picture Quality (Page 53). The TZ2 offers just two resolution settings. Standard and Fine. The Fine setting saves the most information possible about the picture and is much better choice than Standard. If high quality images that can be enlarged is what you're after - Fine should be where you leave this setting. Standard can be good choice for web graphics and simple 4x6 prints if you wish.
These settings do come at a cost however. In the example above, between the 0.3M and 7M pictures, you could take twenty (20) very low quality pictures on the 0.3M setting OR a just single high resolution picture in the same amount of space on the card. This means needing to carry more SD (or SDHC) cards or larger capacity SDHC card if you find you current card is filling up too fast with the high resolution / quality settings.
I hope this helps and good luck! Please rate my reply. Thank you.