Translate the paragraph you want to memorize into English. Memorization will be easier if the text has meaning to you, as opposed to being essentially a collection of unfamiliar sounds. Google Translate is a useful free tool for this, however, the ideal way is to ask a bilingual Spanish speaker to talk you through it. Also, you can look up words one-by-one on an online Spanish dictionary.
Check the pronunciation of all the words in the paragraph. SpanishDict.com is a free resource that gives the proper pronunciation of the words.
Record the paragraph using a Dictaphone, using proper pronunciation, or ask a native Spanish speaker to read it for you.
Play the recording back, and set the Dictaphone to repeat, so that the paragraph loops over and over. As it plays, follow the audio with the written transcription. Use your finger to move over each word as it is being said, and say the words out loud at the same time. Brute repetition is a key to memorization, so do this continuously in 10- to 15-minute intervals, giving yourself a 10-minute break in between.
Read the paragraph out loud. The pronunciation should have become second nature by now. If there are any parts you are struggling with, go back to your audio for reference. Again, use mass repetition to your advantage with the same interval scheme as before.
Test yourself. Turn the transcription over and attempt to write out the entire passage. After each attempt, check the transcription to see if you missed anything. Then cover up the transcription again, and repeat until you can reproduce it perfectly.
Test your self verbally. Use the Dictaphone to record a recital of the paragraph, without referring to a transcription. When done, listen back and check for mistakes. Repeat until you can recite it perfectly.