If you don't own an overlocker, being able to sew a hidden gusset, not only keeps your work neater but it allows you hide all raw edges of the top of the gusset piece. It's not a hard thing to sew, however if you have tried, you've probably ended up with a twisted inner or outer gusset, and had to unpick and re-start again, I know I have in the past.
The way I am going to show you, is the easiest way I have found without twisting seams and attempting to hold all the pieces together and ending up with some pieces stretched. Apologies for the garish nature of the fabrics, I hauled together all the brights so you could see exactly what was going on and did the top stitching in lilac and bottom stitching in black.
Roll up the front piece, and sandwich between inner and outer gusset, ensuring you have the right sides and wrong sides correct. See above.
Turn upside down, and lift the inner gusset back, roll up the back piece and place onto the outer gusset, again ensuring the correct sides are together.
Flip the inner gusset back over and pin together the with the outer gusset and back piece.
Pull out the front and back pieces, and the seams connecting them to the gusset pieces will be hidden. Sew the inner and outer gusset together which will make applying the elastic easier.
The final piece - all seams hidden.