If you remove both side covers (usually two thumb screws in the back on each side), you should be able to see, or feel, inside the front edges on each side of the case. Most cases have two or three split pegs on each side holding the front panel on. Squeeze the ends of the pegs and push them forward and the front panel should pop off. Just be aware that there are going to be a bunch of cables running from your front I/O panel to your motherboard, PSU, and probably fans too. Either take care to note how they're all connected so you can reconnect them afterward, or just separate the front panel from the chassis just enough to do whatever cleaning you need to do without pulling any of the cables loose.
As I said, that works for most cases - yours may be different, in which case you'll need to do some hunting to see how the panel is attached to the chassis.