Herbivores use five main categories of strategies to evade plant defense and consume the plant: mechanical adaptations (such as teeth), biochemical adaptations, behavioral adaptations, microbial symbionts, and host manipulation. All are generally used simultaneously, though to a greater or lesser extent depending on the species. All are generally characterized as offensive adaptations, as the herbivore launches the attack on the plant, except in the rare case of carnivorous plants.
Just like interaction between predators and prey, the interaction between herbivores and the plants they eat is an evolutionary arms race. Plants use various defenses to discourage herbivores from eating them -- physical defenses like spines, efforts to make themselves less palatable, noxious chemicals (called secondary metabolic products) designed to halt the herbivore, and other strategies. At the same time, herbivores evolve various strategies to circumvent plant defense. Current plants have batteries of defenses to use against both invertebrate and vertebrate invaders.
The most universal adaptation used by herbivores to cope with plant defense are mechanical. Herbivores must have some feeding mechanism, teeth or mandibles, to rip off parts of a plant and consume it. This is reflected in thousands of different variations on the simple concept of a tooth, from the tens of thousands of "teeth" in the radula of a snail, to the 32 permanent human teeth. Depending on whether an animal is an exclusive herbivore or an omnivore, its teeth will be more or less sharp or curved, shaped differently to accommodate its personal diet.
Another class of adaptations against plant defense is chemical. Many herbivores produce enzymes that cancel out poisonous chemicals released by the plant when it is under attack. These negate the immediate defenses and allow the herbivore to consume the plant. Then, another class of adaptations take over in the stomach -- different herbivores have different stomachs with different bacteria customized to digest the molecules in their favorite foods. One of the most impressive evolutionary innovations among terrestrial animals of the Cenozoic was the evolution of the multi-chambered stomach, which evolved to digest nutrient-poor grasses.
Some of the most interesting herbivore adaptations to plant defense are behavioral adaptations host manipulation. By eating a plant at a certain time or in a certain season, an herbivore can maximize the nutrition it gets while minimizing the presence of undesirable chemicals like tannins. Some of the most clever adaptations are host manipulation, where the feeder somehow gets the plant to give up its nutrients. This is seen both in the case of gall-inducing insects and human agriculture.