Find an online Swedish alphabet pronunciation guide like the one offered by Tripod. The guide should both show each letter of the Swedish alphabet and play an audio clip of the correct pronunciation.
Practice saying each letter aloud. Listen to the sound clip of each letter and repeat it as many times as is necessary to approximate the Swedish pronunciation. Some letters will be more difficult to pronounce than others. Practice the more difficult letters more often.
Memorize the letters. Make flash cards on index paper with each letter written on a separate card. Say the sound of the letter corresponding to the card. Repeat this process until you have memorized every letter of the Swedish alphabet.