By itself, poner typically has the meaning of "to place" or "to put." So there may be little surprise that over the centuries it has been combined with numerous prefixes: con + poner = componer and the idea of putting something with something; re + poner = reponer and the idea of putting again; in + poner = imponer and the idea of putting in, and so on. (Note that an n before a p is pronounced the same as an m, and thus the change in spelling.)
In fact, poner is at the head of a whole family of verbs with an incredibly wide variety of meanings. And most of them have corresponding words in English — but with a twist. That's because the French equivalent of poner is poser, which also can mean "to place" or "to put," and much of the Latin vocabulary of English came to the language by way of French. So the three verbs listed above in English become "compose," "repose" and "impose." (There are some derived words, however, such as "component," where the relationship to Spanish form, in that case componente, is more obvious.) It is important to remember, however, that meanings of words change over time, so while English may have a word (known as a cognate) directly corresponding to the Spanish one, they don't necessarily mean the same thing. For example, the Spanish transponer can mean to switch two objects around, as "transpose" does, but it more commonly means simply "to change" or "to move."
As mentioned above, poner, like most common verbs, is conjugated irregularly. "I put" in the present tense is pongo and puse in the past (preterite). Its past participle is puesto, which is used with many of the prefixes to form words also. The verb is irregular in nearly every tense, but it's common enough that its conjugation needs to be learned. Fortunately, all the verbs in the -poner family follow the same pattern.
Looking to expand your Spanish vocabulary? Go to the next page to see a listing of the most important verbs derived from poner.