This is one area where you may find varying advice - whether to be the first to give a number or not. Everyone agrees, however, that the first number given winds up being the anchor, which is why I would recommend being the one who puts the anchor out and works from a position of offense.
Many people are nervous that the number they will say is way off base, and that the employer will rescind their offer. That's simply not how it works. At minimum, they will tell you the number is way off base, and your conversation will continue from there.
Consider the scenario playing out like this:
Employer: What are your salary requirements?
You: Given what I could bring to this position, I would expect my annual salary to be $115,000, assuming a standard benefits package.
Employer: WOW, that's more than $20,000 more than what we would expect to pay for this position. Maybe this isn't the right move for you.
You: That's really helpful information to know. Let's talk about total compensation. There could be some flexibility in this number with a better understanding of the total compensation package, including insurance, 401k contributions, vacation time, flex time, etc.
Don't worry that your number will be too high (unless you know the number you are putting out is far higher than the posted salary range for the position - that's a scenario unlikely to work out in your favor). It will prompt a conversation, if nothing else. Certainly, do not give a range in order to hedge (i.e., you'd like to ask for $120k, but are nervous so give a range of $100k-$120k. Guess what? The employer only heard--and will anchor to--$100k).
Giving your number first allows you to have confidence that your needs and ideal salary (with some cushion!) are taken into account, and used as the anchor in the conversation. It doesn't mean you're going to get absolutely everything you want, but it gives you a stronger shot.
The only real risk you have is your number being significantly lower that a range your employer would be willing to offer, and therefore miss out on more money. To ward of the potential for this happening, check whether there is a salary range posted for this position, do some research into how similar positions pay at competitor organizations, and ask how the salary relates to the salary of others in similar positions at the organization. If you're significantly lacking visibility into salary for a position, just keep this in mind and look for opportunities to glean clues regarding what their expected salary for the role would be.