The reason I asked, is lead free is a bit harder to work with, and easily results in joins like your photos.

Ideally you should be aiming for having the soldering iron in contact for less than 10 seconds. For heat sensitive components, even shorter than that.
Process should be - clean tip to remove old solder(that's what the wet sponge is for - the flux burns of, so you want any remnants of solder wiped off), apply blob of fresh solder on the tip, hold tip against what you're soldering, as soon as the solder starts to flow onto the leg/PCB, feed in enough to get a good join aiming for the contact point between tip and component, pull solder pulled away, pull soldering iron away.

Having a decent sized soldering helps. Too small and you have to hold it on for too long to get solder to flow, too big and you risk overheating things if you hold it on too long.