Here's how I learn my dozen or so verses every month or two. It's probably not what the ancient sages had in mind, but it works just fine:
After I've obsessively checked and re-checked that I'm learning the right section, I start learning it from my copy of Etz Chaim, where I can see the English translation right next to the Hebrew. I repeat each line over and over, learning the trop same time as the words, sometimes starting from the end like I used to when studying piano. It's a good way to trick myself; if I started from the beginning, then I might be afraid of running out of time before I got to the end. And even with this method, I still learn the beginning quite well because, well, it's the beginning, and I always forget my plan and start there anyway.
I have the entire Tanakh on my Treo 600, an amazing device. It's the JPS version in Hebrew with incredibly tiny trop and vowels, plus the JPS English translation, which I downloaded for free courtesy of Christian, evangelical Biola University. They offer PDA Scripture on their website in dozens of languages. I doubt they had my particular purpose in mind when they created this database. I really should send them a contribution to assuage my guilt. After I can read the Hebrew seamlessly from Etz Chaim, I practice it on my Treo while on the subway, usually while going back and forth to the gym, trying not to make it obvious that I'm singing to myself in a foreign language, although this might help me get a seat.