Most dictionaries have pictures.
For example, mine has a diagram of the heart and arteries going into the heart. From that diagram alone, a person could learn the meaning of a few words if he knew his anatomy. The pictures for "antler" would give him the names for "reindeer", "fallow deer", and "moose" provided he had knowledge of deer and related animals. Of course, the picture for "anvil" probably wouldn't help him until he learned at least a few supporting words. Instead of just showing an anvil, it shows a man pounding something on an anvil - it's not clear what the word "anvil" refers to (in fact, one would probably think it's a verb describing the action of shaping metals by hammering). Bench mark would probably leave him totally confused, considering the context in which that word is usually used today (in fact, he might think it's a unit of money).
It would be really tough, but I think there's enough clues that a person could learn quite a few nouns, which could lead to adjectives. For example, "green" is the color of grass" (my dictionary is from the 80's and is in black and white, so they just can't show you the color).
I'm thinking verbs would be really hard to figure out (at least using my dictionary which has no pictures describing verbs). Just by frequency, one could figure out the group of words that must be articles, conjunctions, etc, such as "the", "a", "and", "but", etc. The fact that the English language has no gender would make distinguishing between them a lot harder.
The key would be to figure out the sentence structure. If the person is human and you assume the language will have the same general structure, such as a subject, verb, and direct object, then you can figure out which part of the sentence must be the verb, even if you don't know what it means. From that, you could figure out the pattern for adverbs, and the adverbs that are similar to adjectives could even give you some clue of what the verb is. I'm not sure you could actually narrow that down to a specific verb, though, and that would really make getting the whole language deciphered really tough.
I think you'd need a book that actually showed people committing verb-like activity to really decipher the language.