Rooting Samsung Galaxy POP/Mini GT-S5570 is very simple you just have to follow
 this simple steps. And your phone will be rooted in 5 minutes.
Once you have rooted your device, you can install the Best Rom For Mini/Pop by reading
 this post  Which is the Best Rom for Galaxy POP/Mini GT-S5570?
Warning: Rooting your phone voids its warranty. And, this post will not work for phone
 with Baseband version is DDKC1 (see in Settings -> About Phone).
Before starting the root please make sure you have enough battery, about 60%

Step 1:

First download this file> ‘pop 2.3.6.zip‘

Step 2:

Copy the downloaded file to the root of your SD card. [You can copy it anywhere in the SD 
card but, it is easy to find it there]

Step 3:

Switch off your Phone.

Step 4: 

Press ‘Home + Power On‘ button at the same time until the phone starts in the
 Recovery Mode. (In recovery mode, the touch does not works, use Volume keys 
for up/down, Home key to select options & Power key for going back)

Step 5: 

In Recovery mode select ‘apply update from sdcard‘ from the Menu.

Step 6: 

Now select ‘pop 2.3.6.zip‘ from the SD card.

Step 7: 

Let the process complete.

Step 8: 

Select ‘reboot system now‘ option after the completion of setup

Step 9: 

After Reboot, check that ‘Superuser‘ application is installed or not. If yes, you 
successfully rooted your phone.
Congratulations!!! You have successfully rooted your Samsung Galaxy Pop/Mini gt-s5570  :-)