The next step is to solder the new part into place. I recommend taking apart the new part: it is easier to solder the six legs of the reader in the middle (pic?) if you remove the shield on top. This way you will have to put together the sim eject mechanism later on, but imo it's worth it.

Now, the alignment of the sim reader is of paramount importance. If the reader is misaligned, it will cause problems and misery later on. A good rule of thumb: if all the legs are in place over the pads and in the middle, you're good to go. Also, make sure you leave the surrounding ground pads for the shield visible.