I finished grad school and now I will probably be an adjunct but will apply for postdocs again. I want to talk about my research ideas with other people but I am worried that postdocs will work on them, and senior faculty with share the ideas with their own grad students who are looking for projects to work on. How can I share my ideas without this happening?
Basically you can't prevent it. Ideas are free to use. I assume that in "sharing" your ideas you are also hoping to get (and utilize) the "ideas" of others. This is fine.
But you don't need to be an "idea faucet". You can seek collaborations with people and share the key ideas with them. Collaborations are valuable at any stage of a career, but especially so early on since you don't have the support of an advisor anymore.
However, "stealing" ideas is fairly rare. People have their own ideas to work on. The world is there to be explored.
For completeness, it is necessary to acknowledge some kinds of "ideas" to avoid plagiarism charges.
There is the often stated claim that "ideas are cheap, execution is expensive" - that is not entirely true; it definitely depends on the situation. I therefore do not fully agree with my co-respondents that the risk of stealing ideas is small. It does definitively happen, rarer than one may fear, but more frequently than one may hope.
For instance, there are very simple ideas, relatively low-hanging fruits, which are comparatively easy to execute, but which have a large impact. A classic example is high-temperature conductivity where the core idea is so simple that the authors sent it to a lower-tier journal with a trusted editor and to the NYT rather than to the top journals where the short review turn-around time would have been sufficient to replicate and scoop the core insight. This is not a completely atypical example. So, it is definitely a good idea to be careful with the ideas you consider to be critical for your future.
What to do? Share ideas with people you trust and share different ideas with different groups of people. That way you do not put all your eggs in one basket.
That being said, do not be paranoid about ideas, that is not going to do you any good; you simply do not want to be taken advantage of. You can be generous with ideas you either do not have time to pursue or you do not consider essential for your career/development.
And sometimes, you just have to take the plunge and the risk; accept that you might fail to judge a collaborator correctly sometimes; insofar I agree with the other respondents, the times where it works out, will outnumber the cases where it doesn't, if you are a perceptive person.
Scientific friendships are built on trust. Many of them can last a lifetime.
If an idea is developed enough to run with it and write a paper, do so. Only share the key insights with your collaborators, if any.
Less well-formed ideas are unlikely to be worth stealing. In doing research, much of the hard work consists of taking projects from the idea stage to the ready-to-write-a-paper stage. For established researchers, ideas are cheap because they have more good ideas than they have time to pursue. For early-career researchers, good ideas for projects are not cheap, but everyone tries to get suggestions from as expert/senior a source as possible. So I agree with Buffy that the risk of anyone stealing your ideas, even good ones, is small.