I air dry my hair about 95% of the time and my blowdryer barely sees any use. I have a video on my air drying process here and a key part of this process is relying on cotton materials or microfibre towels to dry my hair without damage and minimal frizz.
Why avoid using a normal towel? A regular bath towel has fibres which are far too rough for drying delicate wet strands. Even with gentle patting motions, this material tends to rub up against the hair cuticles which can cause breakage and, it sounds strange, but regular towels also tend to remove too much moisture from the hair. This makes hair (especially if it's curly) dry and frizzy. In comparison, cotton has a flat surface and microfibre materials aren't as fluffy or thick which allows them to remove moisture without causing too much friction on the hair cuticles. As a result, I never reach for a standard towel when it's time to dry my hair.
I've found that you do not need to buy any particularly special products to dry your hair. You probably already have something you can use which won't cost you anything! I personally use old cotton t-shirts (pictured right), sheets or pillowcases.
If you don't have anything you could use but don't want to spend much, you could use try browsing the sale section of any cheap fashion retailer or a charity shop for options. A large mens t-shirt is usually big enough for thick and long hair. If you get a t-shirt with sleeves or straps it's also easier to keep it secured to your head whilst your hair dries if necessary.
There are gentle products specifically designed for drying hair available too. I have purchased microfibre towels in the past (pictured left), some of which are available at little cost from the Poundshop and in supermarkets. If you don't mind spending a bit more BritishCurlies.com has various options like Curl-Ease Towels, Curls Like Us Cloths, Jessicurl towels or Curly Hair Solutions Hand Dry Hair Gloves. Most of these retail above £15 so it really depends on your budget.
I made the switch to cotton and microfibre materials years ago and seeing the benefits for my hair means I'll never go back to using a regular towel.
What do you use to dry your hair?