The best way to break your old habits and start speed reading is to start "reading with your eyes."
There are two main ways that you can do this:
Breaking the Subvocalization Habit
Use your finger or a pen as a guide, and drag your eyes along the text.
Rather than simply following the text you're reading with your eyes, I want you to use a pointer, whether that be your finger or a pen, and start to "drag" your eyes along the text. Take your pointer, put it under the line of text that you're reading, and start moving it along the text. At first, move it along with your eyes at their natural reading speed. Next, slowly start to increase the speed of your pointer and force your eyes to catch up.
This takes practice to get used to, but you'll very quickly find that, even when you're dragging your pointer at two times the speed you usually read, you're still understanding everything that you're reading.
This is the most important step in speed reading. Start doing this immediately when you read non-fiction of any kind. By dragging your eyes with a pointer, you'll start showing your brain that it can move at a faster pace, and you'll find it nearly impossible to subvocalize at the speed that you're dragging.
This is key. For the next three days, try using a pointer when you read, and steadily start to follow the pointer with your eyes rather than the other way around.
Drown out your subvocalization.
This is the most essential step to speed reading, and it also seems the weirdest. Before I describe how to do this, you absolutely need to understand something: hearing the words you're reading in your head has nothing to do with understanding them. Your brain is totally capable of turning text directly into meaning without the help of an internal monologue. In fact, your internal monologue is actually disrupting your comprehension.
Here's the next step: once you're comfortable following a pointer, start counting to three over and over again, either out loud or in your head, as you read. Keep following the pointer with your eyes and attempting to absorb the text above it, and do not, under any circumstances, stop counting to three.
If you fill your mental "auditorium" with counting, your brain won't be able to subvocalize the text that you're reading. As a result, you'll start to absorb the information directly, rather than following the old, slow path that you’re used to following.
At first, this might seem strange, but try it a few times. You will very quickly realize that you're understanding just as much of your material as you used to (often much more) without actually having to hear the material in your head, and you'll be moving at least two times as fast.
You need to keep working at this process. Bad habits are hard to break, and you've been reading the bad way for your entire life. You need to keep working on your pointer dragging and your subvocalization drowning until you feel comfortable with these two methods — they are what speed reading is all about, and they'll take you far.