Depending on the part you buy also the highlighted plastic piece may be not present so you have to take it from the old phone. This piece is crucial, it helds in place the volume and power buttons. To place it simply insert the button (if them have fallen off) and place it in the only direction possible

Peel of the adhesive film and place the battery as in picture

Then connect the battery ribbon cable with the Screen and Power ribbon cables back in place

Then you have to mount back the protective metal shells both on the left and right connectors as shown in the last picture

At this time you can use a new battery for the phone

If you damaged your battery during removal (not shown in this guide) please throw it away and use a new one, this could be very incautious