How do I get newly acquired customers to place their first order?

It's difficult to provide you any real advice without knowing anything about your service/product, or what a 'signup' means (is it a free version of your product, a signup to your mailing list or something else) but generally speaking it can be any of the following reasons:

1) People sign up to get something that they want, but don't need your product, or want to pay for it.

2) Your clients deem the free version to be sufficient and don't want to pay for the paid version.

3) People sign up due to curiosity but the value isn't there for them to purchase.

4) You haven't done a good enough job communicating your product's benefits to your signups.

5) You lack sufficient "calls to action" that would convert signups to paying customers.

Again, this is a gross generaliation, as no-one will be able to give you any specific feedback without having more information about what you're selling.

Hope this helps.
Bryan

You don't have customers. Customers buy things. However, you seem to have at least the appearance of something some people want. That's a good start. Why are they signing up? What are they signing up for?

A survey, or actually speaking with them, about what is blocking them from moving forward would give you some answers. Perhaps what you offer is not exactly as described. Perhaps the users do not have the money (wrong target market) to afford your services. Perhaps your copy is not compelling enough.

If you are getting signups, then you must be appealing to some kind of 'pain' these people are experiencing. But there is a hurdle to be overcome for them to invest money in a solution to get rid of that pain, and your site is not yet doing that.

Well I am not sure that you can call them customers until they buy something. Given the nature of your question I am assuming that you have compelled them to navigate to your site or store front. At this point the answer is simple, but its execution may not be. The answer is to provide a compelling value add narrative to you prospective customers. You may need to figure out who these people are and why they might find value in your product, then convey a narrative that speaks to those needs.