Most abilities will stack. Numerical bonuses are almost always applied before multiplicative ones; If you have a Brim Smith getting a boost on its Artifact’s Attack (which a Dark Brim Smith does), that’s added before the Brim Smith’s 200% multiplier.
Dodge and Death chances, however, never stack; you can’t get 15% Dodge from a Wyvern Windrider plus 45% from Eye of the Thylacine. Each chance to dodge is calculated independently. Likewise for death; if you have a Shogun with Cull the Weak attacking a Weak-afflicted target, he gets first a 20%, then a 50% chance to kill, rather than a single 70%.
Likewise, certain creatures apply rules to the field, and having duplicates of their abilities on the field will have no effect, but these are almost always clearly stated. For example, Bile Slime doubles Poison damage to the enemy team; this effect will never stack, and having two of it does nothing.