Can I make my 04 Honda Civic faster?

I have a 2004 Honda Civic ex automatic that I want to make it faster. But can I? And how?

Sure but speed costs money - how fast do you want to go?

Not much that's why you don't see Hondas racing in the Daytona 500.

It is on the way out.

You can, what you can do depends on your budget.
first up make sure it is all upto date servicing, clean filters, good oil, transmission serviced. Get your mechanic to make sure your sensors like MAF or MAP sensor, and oxygen sensors are operating well and replace if needed.
next step would be a free flowing exhaust (bit larger bore, too big isn't good either) new higher flow catalytic convertor, extractors if you can afford. Then a cold air intake to get air in easier (might involve a new air filter box, also note some shouldn't me used in wet situations).
beyond that you start getting into the real expensive stuff, engine and tune mods or engine swap. Both would cost more than your car

Yes, get a racing header exhaust system eliminating some or all the catylic converters with a muffler at the end > 15 hp right there then get a CAI (cold air intake) and increase another 10hp. Look into more advanced engine upgrades for bigger Hp by adding a turbo charger kit.

No its a honda civic you ricer!

You can. It is called money. And paying a mechanic to do it. Personally you do go fast enough to kill yourself, and faster than any allowable road speeds. The mechanic you choose can tell you what they can do for you. Money is the determining factor

IHE - intake, headers, exhaust is a good start.

If you know how to drive manual should consider getting a transmission swap as well. Also depending on the engine, assuming D series on what you said, could also look into swapping in the K series engine, the K20Z3 if possible.