To improve the details on the planets, you'd need to get an eye-piece with a shorter focal length. I assume your telescope came with a standard 40mm or perhaps 20mm eye piece, which would give you magnification of 22.5x and 45x (respectively). To see nice details on saturn, jupiter or mars, you'd need a magnification of about 150x and more, i.e. you'd need an eye-piece of 6mm or shorter.
For now, consider buying an eye-piece kit, Celestron has a pretty good one for about $150, with a great combination of eye-pieces, color filters and should also include a barlow.
When it comes to non-stellar objects, i.e. galaxies and nebulae, visually you cannot do much without increasing the aperture. The only way to get views you see around the internet is photography, with exposures of 10s of minutes. Astrophotography is quite complex and very expensive hobby with an incredible steep learning curve. If you have a look at the Amateur Astronomy Picture Of the Day (AAPOD) those guys use equipment worth tens of thousands of dollars and have been doing it for a while.
If you have a DSLR camera you could take images of brighter objects using a set of adapters to connect the camera to the telescope (instead of an eye-piece) but you just won't get results close to those you see on the internet.
BTW, most pictures you see on the internet are in "false" color, that is, virtually every nebula or galaxy seen through the telescope will appear gray-white. The only way to make it colorful is to combine exposures taken through different color filter (in a similar manner a color picture has RGB channels combined).