If there were no specific techniques for beginning a composition, composition would likely not be a field of study. Often within composition study, the teacher will provide a set of guidelines that essentially tell you how to start. I am assuming that you are not working with a teacher here, which of course is the "real-world" case, and give you the number one rule I took from composition study:
Setting limits is decision-making, which in turn is composition. You need to go from a blank slate to something tractable. Some limits will nearly always be set for you if you are writing for a particular purpose. For example, if a string quartet has commissioned a piece, the instrumentation is almost certainly the string quartet, so the instrumentation, texture, and pitch ranges available to you are already limited in a specific way. Taking the abilities of the specific musicians into account is also important. If you write a work that one specific musician or group can perform, others will probably also be able to perform the work. It is too easy to write nearly-unperformable music, so keeping abilities in mind is important. If you do not have specific musicians in mind, the preferred option is to find some. If that is impractical, at least keep in mind the skill level of some "average" or "professional" or "student" musician(s) as you write.
Keep a few more things in mind here:
What if my limits don't allow me to use this really cool idea I have?
Then congratulations, you have a really cool idea you can use in a different piece with different constraints. Consider keeping track of those ideas somewhere so you don't forget them!
What if my limits are not working for my piece?
If you set the limits, you can always change them. Don't be afraid to set limits just because they might be too restrictive. You can always change them later, provided they are not set for external reasons.
You don't have to compose the piece in order from start to finish. In fact, you probably shouldn't.
On one choral piece, I had a text I wanted to use, and I knew exactly how I wanted the climax of the piece to sound. I started there. Start anywhere you want. If you are not sure how to connect one section to another, skip it and come back. If you have a melodic (or other) idea, but you are unsure where in your piece it goes, write it down somewhere anyway. You can come back to it later when you know where it fits, like putting together a puzzle. Or, maybe the idea comes from a different "puzzle" entirely. Keep track of it along with your other "cool ideas" from above.
Decisions about form from the start can really help you get pieces finished.
Form can help you reuse elements throughout your piece so that you can get more mileage out of less material. Further, form helps the piece be more coherent and, sometimes, more "comfortable" or "familiar-feeling" to the listener (if that is your goal). Form is nearly always one of the first limits I set.
As implied elsewhere, there are probably at least as many approaches to composition as there are composers. Nevertheless, you can do significantly better than "whatever works," and a composer who tells you that composing just involves "whatever works" either does not fully realize the assumptions he or she is making or does not want to reveal his or her secrets.