As much as I hate this sort of answer… “It depends.” If you don’t have a license of Acumatica, you should talk with a VAR who will be your sales channel for any licensing needs.
That said, you can download Acumatica from https://builds.acumatica.com and install on your local machine or on a private or hosted Windows server, provided it meets the hardware requirements. As a developer instance, you can install MS SQL Developer Edition if you don’t have your own licensed SQL server for development already. (I do not recommend putting your development on the production SQL instance.) For web services development, the downside is that the “unlicensed” development instance only allows only 2 connections to the database which can be a problem if you have multiple people trying to work in the same instance. However, I do all my development locally with a Git repository for centralizing code, and then our Sys Admin uses an unlicensed (2 user) instance on a server for QA testing before we roll code to production. If you need more than this sort of instance, your VAR can assist you with options from self-hosted to cloud-hosted instances.
Acumatica provided training for developers and sys admins all the way to users of each module is available online via Acumatica Open University. While this training is a great resource for getting started, you will want to refer your developers to post questions here or on StackOverflow (tagged Acumatica).
My best recommendation is to get connected with a VAR if you do not have one already so that they can guide you through the licensing and training opportunities. Acumatica can be installed with a Sales Demo option so that you can start “playing with it” as soon as you get it installed. As long as you don’t need more than 2 concurrent connections, it’s basically free for non-production use, but you really should check with a VAR to ensure it is ok to proceed without any sort of paid licensing.