Regarding the "how and with what" questions in the OP, my GF often sits on our couch and instructs me to lay across her lap face-up... with my bare erection right where my bare butt would normally be for an OTK bare bottom spanking. It is humbling to have to take off my boxers and lay across her lap face-up to present my erection for discipline in this manner.
Depending on the circumstances, she will swat my bare erection with her hand, a paint stirrer, or wooden ruler... Or, when either I or my penis have been especially disobedient or disrespectful (i.e. erections/masturbation without permission, etc), she administers a severe bare erection thrashing with a short (8 inch) leather strap or a short (10 inch) hickory switch.
She also has a short flogger-type penis whip (a cluster of about twenty 6 inch shoelace-type leather strips, with a short handle) clipped to the outside of her purse. On a few occasions, when I have been naughty in public, she has unclipped the penis whip from her purse and handed it to me (i.e. at a dinner table with others within watching/hearing range), telling me, "Don't forget to give this back to me when we get home, because I'm going to have to use it tonight."
On one occassion, eating breakfast at her sister's house, she had me "fetch" the clip-on penis whip from her purse in the front hallway and return to the kitchen wearing nothing but my boxers, and of course my boxers did not hide the fact that my penis was standing at attention, already rock hard. My boxers were soon on the kitchen floor and she administered a severe bare penis/erection thrashing right in front of her sister and her sister's teenage niece and nephew! Having my sister-in-law and her kids witness my penis being punished was very humbling.
Also, regarding the "how" ...
She thoroughly disciplines my erection, starting with soft swats (with the ruler, for example) along the top surface (the area that lies on a man's abdomen, when he's laying on his back), from base to head. Then, soft swats along each side of my erection, from base to head. Then soft swats along the _sensitive_ bottom surface of my erection (the area that faces up and is most easily accessible when a man's erection lays on his abdomen, when he is laying on his back), from base to head. These soft swats -- especially along the extremely sensitive underside, moving from the base, to the stretched foreskin, to the frenulum/glans -- are extremely erotic, and I always become even more rock hard than I think possible. Often my penis/erection begins to throb and I feel like I want to explode. But when GF sees the throbbing, she always lectures me that I'm being punished and that if I orgasm, my punishment will be much more severe! At this point, my fate is in GF's hands because she knows that if she continues swatting/teasing my frenulum after the throbbing starts, I will explode... and she will increase the severity of my penis punishment accordingly... which usually means a dollop of Icy Hot on my frenulum and then a severe frenulum thrashing with the 8 inch leather strap.