Here's what happens when you use conventional shampoo: you completely strip all of your scalp's oils from your scalp and your hair, leaving them dry, then try to replicate their effects using conditioner. Most conditioners contain silicones, which make your hair shiny, but which can only be removed from the hair with conventional shampoo. The end result is that you damage your hair with an overly-harsh detergent, then mask the damage with a coating that can only be washed out with more overly-harsh detergent. It's a nasty cycle, and one which shampoo/conditioner producers would very much like you to perpetuate.
As I said in my post on facial oils, if you aren't completely stripping your hair and scalp of all of its natural oils, it won't feel the need to overproduce them and become greasy by the next day. Don't worry, there's an incredibly easy, cheap solution to this problem, which I know you are waiting for on the very edge of your seat!
The first thing you have to do is get past the notion that you need lots of foam and lather to be clean. Just toss that right out the window and don't look back. I mentioned sodium lauryl sulfate (SLS) in my last post as being a Bad Thing. It is, as I just learned on Wikipedia, an amphiphile; this means it has a molecular structure that makes it attracted to both water and fats/oils, which explains why it pulls all the moisture out of your hair. I just thought that was neat. Basically, it's a foaming agent and a detergent, and as I have mentioned a few times, it's not great for you or your hair.
There are plenty of shampoos that don't contain sodium lauryl sulfate (SLS) and won't be as harsh, but why spend money on those when you can whip something up at home in less than a minute that costs you next to nothing?
If you're sick of hearing me talk about baking soda and vinegar, you're in luck, because that's exactly where this is headed (I didn't say it was GOOD luck).
To clean your hair, all you need is a little bit of baking soda and water. I do mean a little bit: just mix one tablespoon of baking soda with one cup of water. That's a 1 to 16 ratio, if you're into fractions. What I do is just put a little bit of baking soda in an old, well-rinsed shampoo bottle, fill the rest with water, and then shake it up before use. To use it, all you have to do is pour some on your head (focusing on the roots of the hair), then scrub it in with your fingertips, then rinse out. That's it. Just like regular shampoo, except I focus more on the scrubbing aspect. Despite that, I find that far fewer hairs fall out and end up in the drain than ever before.
Now, since baking soda is a base and it can rough up your hair shafts and even build up over time, it's important to rinse it out with an acidic compound that will neutralize it and smooth the shafts back down. That's why you take another empty, well-rinsed bottle, pour some apple cider vinegar in it, then fill the rest up with water and use that as your conditioner rinse. It seals the hair shafts right up and leaves your hair real shiny. And as long as you're very careful to rinse it all out, no lingering smell of vinegar will remain.
Should you start using this method to clean and condition your hair, you may find that your hair is still greasy at first. As your scalp adjusts to the fact that you're not attacking it with SLS every day, that greasiness will slow way down, and you may find that you don't even need to do the baking soda/vinegar routine every day. Most days, I just scrub my scalp vigorously with my fingers for a few minutes in the shower, then do a little vinegar rinse on the ends. If my hair starts looking weighed down after a few days of this, I'll do a full wash with baking soda and rinse with the diluted vinegar, and I'm right as rain.
Full disclosure, I do still have a couple of bottles of regular conditioner I'm trying to use up. Before I transitioned to baking soda and vinegar, I was using SLS-free shampoos and silicone-free conditioners, and I still have some of the conditioner. On my finger-scrub days, I'll use a tiny amount of the conditioner to smooth on afterward and it leaves a faint, pleasant smell and probably some extra moisture. Nothing wrong with that, and no silicones to build up and need stripping.
Basically, just do what feels right at the time, and don't be afraid to try new things. Eventually you'll stumble upon a routine that works for you... hopefully one that leaves your scalp, hair, and wallet happier than when you started!
For more information, here's an Instructables about how to go no-poo.