Generally speaking, you have to look at the feature itself to determine how it would stack. If the feature does not say, then it doesn’t stack: you just have two redundant copies of it.
For example, uncanny dodge says this:
If a barbarian already has uncanny dodge from a different class, she automatically gains improved uncanny dodge (see below) instead.
If a rogue already has uncanny dodge from a different class, she automatically gains improved uncanny dodge (see below) instead.
So for uncanny dodge, if you multiclass and get it twice, you get an upgrade to improved uncanny dodge. And improved uncanny dodge also discusses multiclass characters:
If a character already has uncanny dodge (see above) from another class, the levels from the classes that grant uncanny dodge stack to determine the minimum rogue level required to flank the character.
If a character already has uncanny dodge (see above) from another class, the levels from the classes that grant uncanny dodge stack to determine the minimum rogue level required to flank the character.
So a 2nd-level barbarian/2nd-level rogue has both uncanny dodge and improved uncanny dodge, and the minimum rogue level to flank her is 4th, since the barbarian and rogue levels stack for that purpose.
And the barbarian’s fast movement feature also discusses stacking:
This bonus stacks with any other bonuses to the barbarian’s land speed.
Note that this is different from the monk feature of the same name. For one thing, the barbarian class feature applies an untyped bonus, while the monk feature is an enhancement bonus to speed. For another, the monk feature lacks this line about stacking with anything.
For a barbarian/monk, the fact that the barbarian fast movement stacks with any other bonuses to land speed means it stacks with the monk fast movement, since that applies a bonus to land speed. Even if the barbarian feature didn’t have the line about stacking, an untyped bonus (as in barbarian fast movement) will always stack with a typed bonus (as in monk fast movement). Basically, these are two different features that happen to have the same name, which is confusing as anything and really ought to have been fixed when Pathfinder was created from the D&D 3.5e rules, but apparently it got missed.1
So those two stack largely because, despite the name, they are really different features. What if someone got barbarian-style fast movement from two classes, though, or monk-style fast movement from two classes?
For barbarian-style fast movement, the line about stacking with “any other bonus” becomes important: that means it stacks. Without that line, the untyped bonuses from each feature may not stack, because they are arguably from the “same source,” a class feature called fast movement. However, this is an ambiguous, contentious case—many would argue that they aren’t the same source, despite the same name, because they come from different classes. (Note: for typed bonuses, or class features that are not simply bonuses, they almost certainly won’t stack no matter how you argue it—the bit about same source only matters for untyped bonuses.)
For monk-style fast movement, getting it from two classes is redundant: they won’t stack. Nothing in the class feature says it stacks monk levels with any other class, and so they don’t. So you would have two separate enhancement bonuses to speed, which never stack (bonuses of the same type don’t stack).
- Paizo actually did update the barbarian entry—the quoted line about barbarian fast movement explicitly stacking with anything didn’t exist in 3.5. Why they didn’t simply adjust the name to avoid confusion—or make the two features more similar—while they were doing that, I have no idea. I think they should have.
