This depends on the barrel.
You can buy "drop in" barrels that usually drop right in a Colt with normally no fitting needed.
If you step up to a Match type barrel fitting is needed, or if your gun has a fitted barrel bushing even a standard barrel may need fitting.
Usually as long as you're installing a name brand barrel in a Colt and it's a drop in type, you should be able to just install it.
If you buy a cheap or "no name" barrel or have a non-Colt gun you may have to do some fitting even with a standard barrel.