Buy yourself a missile
If you are a multibillionaire or the leader of a reasonably wealthy nation, there are a number of options at your disposal. Probably the cheapest is to invest in a fleet of satellite-killing missiles (which cost somewhere in the neighborhood of $9 million each) and some fighter planes capable of high-altitude flight to deliver them (like the F-16, which is a steal at around $19 million a pop). Currently, only the United States, Russia, and China have this technology, so you’d be entering a pretty exclusive club, but it’s totally worth it. You get a key to a special bathroom at the U.N. and everything.
You’ll also want to get some satellites of your own into orbit as well as building several observatories tasked with spotting satellites that may be spying on you. You’re going to need to plan carefully if you want to be thorough.
Your most cost-effective option is to install nuclear warheads on your antisatellite missiles. This reduces the need for accuracy and will not only kill multiple satellites at once but will also disable many others with an electromagnetic pulse. Time your attacks to catch as large a cluster of satellites as possible. Also, be judicious in your timing. Most countries will consider you nuking their satellite networks to be extremely rude.
If you’re feeling supervillainous, you can skip the missiles and go for space-based weapons. Satellites can be armed with their own missiles or high-powered x-ray lasers or they could just be orbital bombs that creep up on enemy satellites and commit explosive suicide when they get close enough. The Russians developed a system that basically dropped a bunch of debris in the path of enemy satellites to shred them as they passed through at a few hundred miles an hour. If you’ve got the power, the technology, and the time, you can also build ground-based lasers mighty enough to blind or kill enemy satellites.