Learn the syllabery chart. Unlike English, Japanese is a language that relies on syllables rather than letters. Japanese also doesn't have the same range of sounds as English does, although there are some overlaps. Unless explicitly noted, there are no long vowel sounds in Japanese, but there are the same five basic sounds: A (ah), I (ee), U (oo), E (eh) and O (oh). These can stand alone, or can be paired with a consonant sound.
Aside from the nasal stop, N, consonants are always paired with a vowel sound. These are noted on the Hiragana chart, and make up the basic Hiragana alphabet. Practice especially the R sounds, as they are the most challenging for English-speakers--in Japanese, ra, ri, ru and ro begin with a sound halfway between our L and R, your tongue should lightly tap once against the top of your mouth when you pronounce them.
There are some more complex sounds as well. Voicing marks look like small quotation marks (") next to a character, and you pronounce the consonant voiced--so K-sounds become G; S-sounds turn into Z, T sounds like D and H-sounds turn into B. A small circle next to an H-character turns it into a P sound.
Choose a phrase from your phrasebook. If the sentences are not Romanized (translated into English text), use your Hiragana chart to decode them. Note that a dash (--) in Japanese translates into an extended vowel sound, usually translated as a double-vowel; while a small tsu character (looks like a close parenthesis or backward C) indicates a hard consonant sound, usually translated as a double-consonant.
Begin sounding out the sentence. Note that when the final syllable ends in U, that sound is generally silent. If possible, locate an audio file or recording of the phrase being said aloud and start to correct your pronunciation accordingly.
For example, the sentence Sushi wa oishidesu is pronounced Su-shi wa oh-ee-shee-des. It means "Sushi is delicious."