Well, you say you're new to programming so why not take a step back and write a few routines to make sure you're LEDs are working properly and connected well?

Your schematic isn't very clear on my screen but it looks like your LEDs are hooked to PORTB. Something like:
(I usually work with 12F683 so this code may not be totally correct.)

STARTHERE:
TRISB = 0
PORTB = 0
PORTB = %00000001
PAUSE 100
PORTB = %00000010
PAUSE 100
PORTB = %00000100
PAUSE 100
BLAH BLAH BLAH


GOTO STARTHERE

This way you know the LEDs will work once you get the right code.

Also, I see it worked in Proteus but if the real world LEDs need more voltage/current, looks like a 330ohm current limiting resistor, than 6mA the LEDs may never come on no matter what your programming looks like.

Could you post an updated schematic if none of this helps? Sometimes a second set of eyes helps find problems hidden by the forest.

Best wishes