Although the other answers have merit, I believe that your question is a little more complex. To prove that another company is “making, using, or selling a patented item without the permission of the patent owner” (ie. infringing your patent), you would most likely have to file a lawsuit in federal district court. After the litigation begins, there is a process called discovery, were both side get to collect evidence about the alleged infringement. And to make it more complicated there are several types of patent infringement possible:
Direct Infringement: is when an infringing product is covered by at least one valid independent patent claim and is manufactured without permission.
Indirect Infringement: is when infringement is induced by encouraging or aiding another in to infringing a valid patent claim.
Contributory Infringement: is when another party supplies a direct infringer with a part that has no substantial non-infringing use.
Literal Infringement: exists if there is a direct correspondence between the words in the patent claims and the infringing device.
Even if an invention does not literally infringe any valid patent claims, the company may still be infringing the patent under the doctrine of equivalents (which is way to complicated to answer here).
If there is enough evidence to prove any of the types of infringement listed above in a court, and all the follow on appeals to various higher courts, both here and possible in a variety of other countries, then you have proven that your patent was infringed. Of course, this costs millions of dollars, and can drag out for years. Just ask Apple or Samsung.
Astronomy and Law 