You don't. A (sc)ramjet doesn't have a compressor, as the forward velocity of the jet provides the necessary pressure.
Most thermal engines do work by expanding a gas. In many cases, this gas expands against a piston, and the piston converts the heat energy into mechanical work. A turbine does not contain a piston to expand against, and the walls of the turbine offer neither movement as required by a piston, nor thrust even if they could move. Thus, the combusting fuel must expand out the front and the back of the engine. Obviously, expanding out the front is undesirable, as that provides negative thrust. Nor is it feasible to place a piston there for the gas to expand against. The solution is to create a virtual piston out of air, by squeezing incoming air so that when the combusting fuel expands, its only choice is to expand out the rear of the engine. The fact that this also improves oxidizer flow is a virtuous benefit.
When the fuel combusts, it increases the pressure at the site of combustion. This pressure wave expands spherically, because it doesn't "know" which direction it is "supposed" to go. The walls of the turbine confine the pressure wave in the radial direction, so all of the pressure must travel axially, both forwards and backwards. If the pressure in the front of the turbine is lower than the pressure created by combustion, then some of the exhaust will flow forwards through the engine, which I think we can all agree is not the desired behavior. The only way to prevent this forward flow is to ensure that the pressure in front of the combustion chamber is at least as high as the pressure created by combustion itself. And that establishes the minimum pressure you must generate just to make the combustion products flow strictly out the back of the engine.
So yes, the compressor is essential to guarantee that the exhaust only goes out the back of the engine, and not the front. And yes, the compressor helps improve oxidation of the fuel, just like a super/turbocharger in a piston engine (and why the original jet engines were called "turbojets"). And yes, forward movement of the engine is sufficient to provide compression, provided adequate airspeed.
Although a ramjet can theoretically operate at speeds as low as Mach 0.5, they are typically considered optimal between Mach 3 and Mach 6.