1st, you will need the official 1.50 and 3.52 sony eboots. get them here;
okay, now that you have both of em, put them in one folder on your desktop and rename the 1.52 eboot to 150.pbp and the 3.52 eboot to 352.pbp
okay, now get the 3.52M33 installer and put it in your "Game150" folder found in your psp
run it in your psp and follow the instructions.
oh! and put the eboots you downloaded in the same folder where the updater is found.
after it dumps the files, go back to your xmb and back to the game section of the menu and go to memstick, there will be a new icon, "3.52M33 update" run it and wait for your psp to finish installing it. when it is done, youll hafta manually reboot your psp.
now that you have 3.52M33, update it to the latest patch of 3.52M33, which is 3.52M33-4(the most stable one)
here it is;
put it in your game150 folder in your psp and run it.
you should now have 3.52M33-4
i suggest you dont go to 3.71M33 yet. it COULD CAUSE IRREPARABLE BRICKS. and with my experience.. is very unstable. i suggest you stick with 3.52M33-4 1st.