You've got your Canon, Nikon or whatever has a built-in flash perhaps, and maybe you have purchased a speedlight to go with it. But you notice that the photos look pretty much the same, flat and casting unnatural shadows which pretty much "look like flash". It's time to upgrade your studio lighting!
1. On the cheap; you can extend the capabilities of your speedlight/s with a remote trigger. There are tons of them out there now, radio slaves that are fired off by your camera hot shoe. Sometimes they are even built into the speedlights themselves. Mount the flash on a light stand, and you have off camera lighting to put shadows in a more pleasing place approximating sunlight. Buy the extra umbrella hotshoe bracket for the flash and you can bounce that light into an umbrella or off the walls, ceilings. This can be a very effective soft, broad light. One of the problems with this setup is you will eventually run out of juice and your flash recycle times get very long; sometimes you get underexposed images if you are trying to do a stereotypical "oh yeah baby, make love to the camera" while popping of 10 frames per second. You can increase the recycle times of your speedlights with external batteries like the Quantum packs; they replace the batteries with a fast recycle. Beware though, this juice popping like crazy can actually melt your speedlight. I've done it.
2. Invest in studio lighting with monolights or a pack setup. I have been a huge fan of White Lightning monolights (Paul C. Buff) and their wireless trigger/controller/meter system. The lights are powerful, sturdy and economical. They are a US company with fantastic support. I've had them replace at no charge parts like capacitors that wore out within three years. Prompt and friendly...the best.
You can start with a single monolight and work your way up to multiple lights. If you start with one and learn to bounce light with reflectors and walls, you can really do wonderful lighting. Complexity does not necessarily help. If you have mastered one light and reflector, work your way into a hairlight and fill light/background light. Good thing is with the White Lightnings you can variably adjust any strobe remotely with their Commander; so you can buy three of the same lights and handle all of the typical lighting scenarios. They also sell light stands and the modifiers that fit them. They are a little more expensive than some of cheap JTL systems, but the quality is worth the extra price. I have had my WL for almost 10 years and they have seen quite a bit of action!
The budget minded photographer might start with the Alien Bees line also by Paul C. Buff which are quite a bit cheaper. I have the Ringflash and a AB1600; they are powerful and have the same features and control capabilities as the White Lightnings pretty much, but the housings are plastic. They are still super functional and I've yet to break one.
The beauty dish is awesome and inexpensive, and the spot grids are a must to push bands or circles of light on the background, hair or side. They fit both the White Lightnings and the Alien Bees. Here is an example of a spot grid and a purple gel against gray seamless paper.
3. Look at other light modifiers like Photoflex softboxes once you've got your basics down.
Learn these techniques and more with my "hands on" Photography Mentoring session.