Smooth edges on .gif files (outlines/transparent backgrounds)

I’m just starting to get beyond the basics with Photoshop, working through a number of tutorials and picking up lots of handy hints and tips.

One thing which I continue to struggle with though is the outline on .gif files on a transparent background. I seem to lose all the smoothness on the edges and as a result my final image’s quality is very disappointing.

Are there any good tips for getting better results when producing the final .gif file?

P.S. I know about .png files but as some older browsers struggle with them I’m not using them at the moment.

Image edges are matted (using anti-aliasing) to background color you specify.
Such a GIF image has a sort of a “halo” of the pixels which help blend it into the background smoothly. But at the same time, on the different background color they form an ugly jagged effect.
Unfortunately, it isn’t possible to make a smooth, transparent GIF image which will look good on each background color. You will have either to accept the jagged edges (aliased) or prepare additional images for each different background color.

I am a beginner too -It can be perplexing!
For a great/simple explanation about GIFs check this tutorial!!!

Wise-Women: Tutorial: Optimizing your Transparent GIFs in PhotoshopThe Matte is the color against which the edges of the transparent GIF will … Choose Paste as Pixels, and to preserve the smooth edges of the graphic, … - 31k

Transparency is good in GIF if you don’t use anti-aliasing. so you should consider that factor; having too much rounded corners and/or too-detailed colors on your file can produce the least impressive results on gif transparency