How much time does it take for Finasteride to show some effectiveness?

It may take several months to see the effects of Propecia.  Most say about 6 months.  To see it "results" may mean slowing of hair loss to some growth.   Not all patients re-grow hair on Propecia.

It takes about 6-9 months to see results - if they are going to occur. The first few months may even be associated with some degree of increased hair shedding. By month 3 most men who respond to finasteride notice that they have less daily shedding. Keep in mind please that finasteride may help some men stop hair loss but not regrow hair. So if your hair density looks exactly the same as today in 1 or even 2 years, this might indicate that the medication is effective. Without the medication, more gair loss might have occured.

Finasteride does begin to reduce DHT immediately. However, rejuvenation of the hair follicles may take several months (4-6) to ensue. Once it starts, then it will be maintained throughout the time of use. Patience is a must.  

Finasteride (Propecia) takes about 6 months to have a visible effect.   It is true that Finasteride blocks the DHT receptor quickly, but the process for hair restoration is much slower.  
As DHT is blocked, the tissue in and around the hair follicle changes from a growth suppressing to a growth promoting environment.  In addition, the affected hairs (both dormant and miniaturized) need to enter into a more normal growth cycle.  All of this takes time.   
My advise would be to continue with the Finasteride (barring any side effects) for a minimum of 6 months to see what kind of impact it will have.  Right now Finasteride is one of the only medications on the market that can block the genetic reason for your male patterned hair loss - DHT.

It takes a minimum of 5-6 months to see photographic improvement using finasteride.  It's very important to take photos when you start.  Keep in mind that there are two goals: slowing down hair loss progression and improvement. About 50% of finasteride users will see more hair growth, and the earlier one starts it in their hair loss potential, the better results.  In my 20 years experience prescribing finasteride, because it slows down hair loss progression for up to 90%, the majority of my patients using it  have more hair than when they started.

When this drug works (it does not always work to reverse hair loss) it usually takes about one year to see the value of it

It takes 6 months to a year for full results. Remember in many cases you may not notice a big difference because Finasteride is primarily sliding down your hair loss which is visually tough to see at times. Remember 100-150 hairs fall out everyday going through the hair cycle.