One thing to keep in mind is that NOBODY has EVER totally eliminated algae from their tank(s). It's all about keeping it to a dull roar. You have to learn a few basic concepts and I'm sure that you'll be up and running in no time.
Keep these in mind:
1) Plants and algae are always competing for survival. If you have too little plant mass in your tank, you'll be leaving more nutrients in the water column for the algae to feed off of. Now that your tank is dominated by algae, you'll have to sort of "hit the reset" button to get it in check. Some people like to do a black-out and leave the lights off for a day or two. Others like to hit the tank with some hydrogen peroxide. Still others prefer to overdose SeaChem excel to take care of stubborn algae problems. Most people (including myself) like to remove the algae manually, then throw in some otos or SAEs to keep the algae re-growth held back as much as possible.
2) Circulation and nutrition are a must in any planted tank. The main purpose for increased circulation is to circulate the nutrients within the water column throughout the entire tank. Remember, plants need nutrients to grow. If you can get the nutrients to the plants through proper circulation, then the plants will use up the nutrients and leave the algae to starve!!! You'll be in good shape if you can get ahold of some method for dosing nitrates, phosphates, carbon dioxide, potassium, and trace elements (I suggest dry fertz. Look here
for a good, quality source). Those are the basics, but they are also sort of prerequisites to a quality tank, IMHO.
3) Lighting. You mentioned the impact of shortened or lengthened photoperiod in your introductory post. It's not too complicated really. Plants need light to grow. Plants use up nutrients while growing, thus outcompeting the algae. I've read somewhere that a photoperiod that is too long can result in plants "leaching" out nutrients over time. This can result in a beneficial environment for algae growth.
There is so much more to learn. I suggest that you scour over Rex Grigg's website, then perform some google searches to see what you can find. Algae is a never ending battle, but you can eventually get to a happy equilibrium if you put the correct variables in play.
EDIT: I forgot to mention how to introduce carbon dioxide. In your situation (with a 44g) I would have to suggest pressurized CO2. The initial setup cost is pretty high, but I seriously doubt that DIY CO2 is going to be a realistic approach for that size tank. You can find CO2 cylinders on ebay for <$60 usually, and a regulator can be found on the SnS here. I won't go into the specifics of CO2 because you can find TONS of info on this site.