Contact them as soon as possible, preferably via phone or other immediate communication mechanism rather than E-mail, which can be ignored. The longer you leave it, the more likely a misunderstanding or miscommunication could see another candidate take the position or you be placed in the "too hard basket".
They key here is not to push for a quick resolution but to (1) understand the process and (2) know where it is at. For example, find out who is driving the discussion of your salary internally in the company. It is probably the hiring manager but it may be the recruiter or HR. Ask them when they will have a decision and how they will notify you. As Joe Strazzere said, this process can take a long time but that does not mean you need to stay in the dark.
It also shows your interest in the role, which is not to be understated.
I'm not sure how salary negotiation is done.
It is an art as much as a science but remember the following:
- Know how much you are willing to be paid and at what stage to walk away from the negotiation. If you are not prepared to walk away, the other party will likely sense that and take advantage of it.
- Know what you are worth. Do some research on similar positions in the industry. Some companies will pay more, some less but have a rough idea.
- Know what the other party wants and how you meet those needs. Stress how hiring you benefits the company, not the other way around.
- It is a business transaction, not personal. Particularly in senior or management positions, you will be expected to be able to negotiate. Start now.
- Be flexible. Maybe you cannot get the salary you want but you can get more leave or a training budget or can work from home. Similarly, to give you the role you want, the company may ask you to take on more responsibilities or tasks.
- As Lawrence Aiello said, never give a salary range. If you say from $X to $Y, the company will hear $X. Indeed, if you want $Y, say you want $Y + $5 (or similar margin) and allow yourself to be talked down to $Y. Indeed, try not to give out your salary expectation early and never tell them what you are earning now, as it is irrelevant to the new position.