Best way to shrink an image?

[Stuarrt]

Heyyy
So I'm trying to shrink down my logo to fit nicely on my banner, but it comes out horribly pixely. How do you guys do it? I see animated banners with logos on them, and they seem perfect.
Any help would be greatly appreciated

 

[Ivain]

Don't do it all at once. Scale it in steps, and sharpen or blur as you think is appropriate, either using a filter or a brush to do it.

 

[TellingMom]

What program are you using?