To make your Chao like you, and adore you, you should be nice to them.
Pet them and hug them to show your affection.
Remember to feed them! To do this go up to a tree and shake it by holding 'B' and moving the analogue stick around.
Once some fruit falls down you can give it to your Chao and it will start to eat it.
An important thing to note, is the differences between the Dreamcast and Gamecube versions.
The Chao found on the Gamecube version of the game can have their personality altered much more.
For example, pet and hug your Chao too much on the Gamecube version and it will become spoilt!
But on the Dreamcast, it will not matter. The site will cover these Gamecube personality differences all in the Gamecube section.
Chao also react to different characters you use. For example if you always look after the Chao with Tails,
and you treat it well, it will begin to like Tails more than the other characters. It will run up to him
and look for attention, and even draw pictures of the favoured character (if it knows how).
Likewise, if you are very mean to a Chao (on purpose or by accident) it will start to despise that character.
When I raise Chao. I am usually only one hero character, and one dark character (in my case I use Sonic and Shadow).
This way the Chao can get used to seeing them all the time and will always feel happy around them.
If you treat your Chao very well, it will reincarnate for you when it dies.
(on the Gamecube, the amount of reincarnations a Chao has had will be known as "transformations").
For more information, see the section entitled 'Death'.
NOTICE: in the picture on this page, you may notice what looks like 2 Chao holding hands and skipping together. Chao do NOT do this in the game. The picture on this site is from the official Sonic Team website, when it posted a lot of pre-release screenshots. Therefore most have come to the conclusion that this Chao action was either removed from the final game, or that the Chao are actually walking normally, with one slightly behind the other causing an optical illusion.