The best way to go about it is to look at other sites, find what you like and what you don't like, and think about how you can use those techniques in your site.
I don't just mean thinking "that site looks good" - look at what makes it good. Is it the colour scheme? Is it the typography, the layout, the spacing, the volume of text? Is it the graphic elements or the effects? Is it the way they've set the menu up? Is it little things like having slight, almost imperceptible, gradients?
I know it's old hat to a lot of people, but if you're new to the game it might be a good place to start - www.csszengarden.com has a lot of quite intensively graphic designs, which may be a step too far for you, but it could give you some useful tips to make a start with.