My method has changed with time. I don't think that my current method is inherently better, it is just better now for my changed mind. I used to break up an aliya into roughly 1/4 column length segments and practice the whole segment with vowelizations and intonation marks, and then go ahead and try it on the Torah-like printed side. I would go back and forth over that segment until I was comfortable with it (but not necessarily perfect) and then move on to the next segment. When all segments were done, I would go back and try to perfect the aliya as whole.
Today, I just tackle one pasuk at time, perfect it, and then learn the next. Each time I perfect a new pasuk, I rehearse from the top of aliya again. If the Aliya is longer than average or has a convenient breaking point, I will divide it and not return to the top of the aliya, but the top of the segment, as I go through the process.
For example, I just read two aliyas today in Parshat Mikeitz, the 3rd and 4th, that I previously did not know. With the third, I always went back to the top at the end of each newly learned pasuk. With the forth, I broke it up into two portions. When I got to he point of "VaYar Yaakov", then from there forward I only went back to that pasuk as I learned the remaining verses.
I reached a degree of minimal proficiency° for these two aliyot on one Shabbat Afternoon. For me, that's what works today. There was a time I was more efficient, (and using my older method) but after going back to studying new Torah portions after not having taken on anything new for several years, I found that I just couldn't learn like I used to, both in pace and in method. Through experimentation, I know this is what works best for me at this time. - It may not do anything for anybody else.
Advantages I find to this method now: (1) Taking it a pasuk at a time allows me to quickly commit to memory that one segment. (2) Rehearsing from top as I go along keeps me from forgetting the first pasuk by the time I get to the last.
It has a side-effect: (3) When asked to lein I will more readily take on two short aliyot instead of one long aliya for efficiency reasons.
° Degree of proficiency: The first time through, I may know it on Torah side for that short while and while reading it slowly, and also while correcting myself but without looking back at the vowelizations and intonation marks -- making for a very choppy reading. If I put down the tikun and don't look at it again until the next day then something has been lost... and I need to relearn parts. Then there's the pressure element. I have found that just because I can read it perfectly at home, doesn't mean I won't botch it when I get up to do it in public. It takes me a great deal of rehearsing to be able to go up to the Torah and do it well. By the time I am satisfied with my degree of proficiency I will be able to visualize most of the words with the intonation in my head as I read it. I will also have a bunch of cues that come to mind just by seeing the first couple words of the pasuk (i.e. okay.. here's the one where the first occurrence is "et" and the second occurrence is "ait" or "Paroh and "Pharoh", etc.)
[EDIT BY AARON 12-20-2009] After some more thought (and some sleep) I decided to see if I can formulate and expand what I related above:
Learn it in chunks that you can readily commit to memory. Only you can determine the right chunk size for you. Reading the entire aliya through over and over again will not get most people far (unless it's a very short aliya)
After you learn a new chunk rehearse from the beginning again. The reinforcement helps retention and it also will allow you to see what you've learned as one flow, and not thinking of it at the end as multiple sub-sections that might introduce unwanted pauses as you read the entire aliya.
To echo what Shalom said, read it out loud. Some people may be more auditory, some more visual, but I take advantage of both. Practice out loud in the same tone, same pace, and about the same volume that you will use at the shulchan. Even if you don't get the sense of an internal recording - it will still build your confidence so that when you get up to the shulchan, you're not doing anything different than you did in your practice readings.
Understand what you are reading. Knowing the meaning will help you know more naturally where the pauses in the pasuk are. The pauses break the pasuk into even smaller chunks, and it makes learning what falls in between the pause points even easier. Also, it's hard to explain, but sometimes the intonations just seem to fit with the meaning of the words.
Like any other learning, it's best if you're not cramming. If you know it decently, a week before you have to read it, you can spend the rest of the week just reading it over once on the side with vowelizations/intonations and 2 times on the Torah side a night until Shabbat morning. You'll be amazed at how much more comfortable you are with it. You'll find the spots where you might be having difficulty work themselves out over the course of the week. Also, with each night, you'll find yourself making minor perfections that you might have glossed over the first time, (stuff they wouldn't have corrected you on) like all the Paroh and Pharohs. Added bonus, The jitters are gone - and that's a biggie so making one mistake where the gabbai corrects you doesn't you throw you off your game.
(I also do the hand motion thing Shalom mentioned, I don't know if it's a learning aid, or just a left over habit from watching my bar mitzvah teacher as he was trying to get me to understand the nuances of the intonations.)
It is entirely possible that my method is only suitable for myself, but I am happy to share, and if anyone else finds it useful, post about it.
P.S> I never understood Ba'alei Kriya, who are picking up the Chumash between aliyot. At times, when I have not had enough time to practice, I have tried that, and it just doesn't help me. Either I know it cold before I get to shul, or I just don't know it like I should and a last minute scan while hearing the gabbai make a Mishberach isn't going to help one iota. From what I have seen, this holds true for many but not all others... and you know you're likely in for a long leining if they holding the chumash.. particularly if they are holding up the start of the next aliya so they can finish their scan.