Professors, at least those at top schools, tend to receive many applications, probably hundreds if not thousands every year.
The best way to get their attention is to find people with good reputation and existing relationships as your references.
The best way to get them ignore you is to send out blanket spam-like inquiries to everyone.
Look at the professors’ websites, which may already spell out whether and how to contact them, and other useful information like their research and style.
It is to your benefit to read these, as you want to find someone with matching style and interests, and the professors want to know why they should pick you.
The best time to contact the professors is around the time you are preparing your application materials, so that you can discuss potential research directions which you can incorporate into your research statement.
If you have a chance to meet them earlier, like in a conference, it cannot hurt to introduce yourself, but in general if you contact them too early, they might not remember you later when they review the applications.
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