Phonemes are the blocks on which language is built. They are the sounds used to construct whole words. There are certain rules which govern phonemes, such as whether a vowel is hard or soft. Some phonemes are also made up of two letters that, when merged together, make a different sound than either would make on it's own. For example, "sh" and "th" both make sounds that are only vaguely related to letters used. Articulating either by separating the letters gives a different sound than the phoneme actually makes.
Morphology follows phonemes, which dictates how phonemes can be put together to form words. One example of morphology in English is that all words must have a vowel. Also, certain phonemes can follow each other, while others rarely or never follow each other. "Sh" and "th," for instance, never follow each other in a word, but almost anything can follow a vowel. Most of the time, vowels do not follow vowels, but there are rare exceptions.
Syntax is the specific property of putting words together to form sentences. Rules of syntax in English include each sentence having at least one noun and one verb. However, there are many exceptions to these rules, as they are often understood by the speaker, even if the speaker cannot articulate them. Rules of capitalization and punctuation are also used to denote syntax in written language. In spoken language, they are generally simply understood by both parties.
Semantics have the least concrete rules in linguistics. Semantics refers to how sentences and word combine to make meaning through syntax. These rules are constantly in flux as speakers use words in new an innovative ways. They can also be used to argue that the actual meaning is different than the intended meaning. Ultimately, semantics are a combination of all of syntax, morphology and phonemes coming together to create meaning.