How can I add a recepticle to this junction box full of push splices?
Good news and bad news.

The good news is, this is very strightforward.  This box is being used solely for distribution.  There are no switches involved here, so you have the good luck that the wire colors happen to match up to wire function.  

All these wires aren't just sitting here waiting for you.  They all are already doing a job.  One cable (black/white pair) supplies power and the other ones take power onward to places where it is being used.  If you separate them, those other places will no longer have power.  To add a load here, you'll need to add its black, white and bare wires to each group, and keep the others still together.  That means putting 5 or more wires together.  

Stab connectors

The wires are going into jab/stab connectors, which are full. You cant add wires, and they can't be used twice anyway. 

To remove each wire, grip the stab connector firmly and pull the wire out firmly while twisting slightly (45-90 degrees).  If the connector has a release tab, that may help.   Start with the longest wires until you get the hang of it; don't twist the wires exscessively as you don't want metal fatigue.  Do not simply cut the wires, because wire length is precious.  

The stab connectors are single-use and there is no saving them.  Into the trash they go.  They make "lever operated" connectors that are far more reliable, and they can be reused.  For novices, I recommend connection styles made for re-use.  

However, stab junction blocks have one merit, they can take as many as 8 wires.  

Box fill

The bad news is the box is getting pretty full.  We calculate box fill based on cubic inches.   This 4x4" deep box has 30.3 cubic inches.   You are working in 12 AWG wires (do not use 14 AWG wires here!), and those take 2.25 (2-1/4) cubic inches per wire.   

All grounds count as 1 wire.  All cable clamps count as 1 wire. That accounts for 4.5 cubic inches, leaving 25.8 cubic inches.  That is enough for 11 black and white wires.  You have 8 already, so you can add one more cable here before "cubing out". 


You can get yourself more cubic inches by adding a "domed box cover" (4-10 cubic inches)  or a "junction box extender" (21 cubic inches). 
Another option is to add a receptacle here.  They make 10.2 cubic inch domed covers with a cutout for a receptacle.  A receptacle or switch costs you 2 wires' worth (4.5 cubic inches), but when added to the box, you have just enough room for 14 wires.  (7 cables).  


Further, certain receptacles allow "screw-to-clamp" wire attachments (back wiring under the screws, tighten to clamp). These take 4 wires per side, so you can use this type of receptacle to splice 4 cables into each other also.  
if you need more than 4 connections, you can "pigtail", run a short wire  between one splice group and the other.   Pigtails count for 0 cubic inches.