They don’t have “taste buds” as in vertebrates, but they do have plenty of receptors that allow them to taste. Keep in mind that generally, the taste and smell sensations are tightly-linked in insects (but it varies: bees smell much more than they taste, for example). Note that I’m basing this answer mostly onDrosophila, the most studied insect, but it should be applicable (with variations) to other insects.
All over the insect’s body are hairs, most often concentrated on the legs and wing margins. These are all taste hairs and taste pegs, and it’s where most of the tasting is done: it’s why a fly will walk on your food, for example.
The maxillary palps (the segments of the maxilla, one of the mouthparts) contains basiconic sensillae, which are responsible for detecting sugar.
The antennae obviously have the most of the chemoreceptors, but most are exclusively for smelling. There are basiconic sensillae there, but they’re for detecting CO2, either by smell or by taste (they’re called the same because of the similar shape). They also smell out food. It’s worth noting that the proboscis (the “tongue”) also has taste hairs used for detecting CO2, but here’s the funny thing. CO2 detected by the antenna elicits an avoidance and alarm response (it means a vertebrate is around and about to eat the fly; mosquitoes have the opposite reaction, it means a blood meal is close by). But CO2 detected by the proboscis promotes an attraction response: it means fermentation is happening, which means that the food source is sugar-rich and very energetic, so it’s good.
There are also coeloconic sensillae in the antennae, responsible for detecting water (smell or taste, we don’t know) and smelling various food odours. (A third type of sensilla, the trichoid sensilla, is used for smelling pheromones; in moths, there’s plenty more of them, used for smelling plant volatiles, useful for finding the host plant).
Note that nowadays, we can also follow the sense organs using gene expression. The main gene family for tasting is called the Gr family, and members of it are expressed in the tarsi (last leg segments), in the proboscis, in the cibarial organs (the “mouth”) and the antennae.