Yeh my hair is VERY thin. Always has been. I've grown it long and it looks really tatty and fragile so I keep it tied up!
Been on finasteride for exactly 9 months (to this very day) and I'm pretty sure it has thickened my hair, although it was so thin naturally that I'm not sure how much thicker it can really get.
Best thing for fine/thin hair is a good thickening shampoo. I use Elvive "body building" for men. It does add more weight and body to the hair. I think if you have short hair it will work better. Long hair tends to highlight thin hair towards the ends.
Good luck.