An engine is an air pump. If you want to make more power with the same sized pump, you need to make it ingest more air. The two ways of doing this are improving it's breathing efficiency and shoving air in forcibly, wether by mechanical or chemical methods.
If you are going to forcably induct it, then start working on the breathing efficiency. Toyota did a pretty good job with the engineering, so the first and easiest places to start are where you think the company would compromise performance and cost. Places that come to mind are the intake and outlet of the motor. Essentially you are making the engine breather easier.
Be careful with cylinder head work. Air is a picky fluid and too much adjustment to the passage can reduce the actual flow in a motor. Specifically in a normally aspirated motor, air velocity and high-lift air flow are more important than the pure volume of air flow capacity at any given moment. The air is traveling across a very inefficient valve system (the single biggest loss in efficiency in a motor, even moreso than heat) and does not take a path anywhere near linear; as such the shape of the port and the thorat and seat area are extremely picky and an inexperienced hand and a die grinder can do more damage than one might expect. If you are not a professional or experienced in the real-world effects of port shaping, I'd stick to the "polish" half of port and polish. A good bit can be gained simply by cleaning up the castings and port areas and making the airflow smooth and uninterupted. It certainly is not an exact science. At least one a mortal could afford to model, or do with a die grinder for that matter.
Standard abrasives is pretty much THE name in automotive abrasives, as lobuxracer said. Just don't go crazy.
Also, make it breathe better before you make it breathe more!
If you want to gain power other than improving the moderations of economy required to sell such a car to such a market, then you will either have to (not preferably) break some laws, improve the design of a certain component, or upset the balance in the engine's performance. What I mean by that is you can add XXX mod and get 5hp peak but lose 5ft*lb in the 2000-4000RPM range. This isn't desirable for some applications, but if peak power is what you are looking for than it may be a good thing. Getting a free and overall gain is, as said before, a matter of improving the engineering or moving beyond the law-based design specs for a certain mechanism.
Obviously we all have to live with legal restrictions as far as emmisions and the equipment securing it's ensurance, but you can legally tweak a part here or there to get a few 'extra ponies'.
"Beginner mods" then. I would also like to back up the chassis tuning part. If you don't mind the downsides of a sportier suspension then improving the mchanics there can make the car feel a lot better. Akin to this, I'd like to mention that a well-trained limo driver can make the people in the back feel like they are speeding when the hypothetical Mr Collinsworth says "Step on it James, we're late for the ball" by applying the brakes more sharply, using more throttle and turning in smaller radii later. He doesn't actually have to break the speed limit!
Back on topic (again) getting a nice exhaust and intake system can improve the acceleration and top end of the car, and in rare cases the low-end if the said modifications take this factor into mind (few do). Those are typical first mods and they are good ones.
One last little tidbit: unspring weight is the bane of a car's performance, specifically in stopping, accelerating and turning. Working on that can make the car a lot more fun to drive.