Every good software customization starts with a good plan. We have been in this business for 41 years now, and there are a couple universal truths to installing ERP systems.
First of all, by the time your company is really ready for an ERP package you have probably tried and suffered through three or four lighter weight systems that didn't fully meet your needs. I think it's fair to say that when you implement ERP, you want all of your needs met. That just might not be a reality without some customizations. For larger organizations, Odoo in my experience is about a 95% solution. The final 5% will be small tweaks and adjustments to the out of the box version.
The second truth is that when it's time to customize, everyone in the company is going to suddenly become a software architect. You will need to head off that line of thinking by designing a good plan for the development you will commission. We have written about this before in a previous post if you want more information on how to prepare for the customization.
After the customization is complete here is a good testing plan:
Partner Test - The partner needs to review your problem statement and expected outcomes before you ever see the work. For most Odoo partners, there are probably two people that should be involved in this process. The first one is your Project Manager, who will test for the functional fit of the customization to ensure that the logic is correct and meets your needs. The second person to test should be the partner's lead developer or development manager. This person is checking the integrity of the code to ensure it meets their quality standards.
Alpha User Test - This is the first test by your team. If the logic is complex, this can usually be a guided test by the partner. The partner should show you the steps to using the customization and gather feedback related to whether they have addressed the problem statement correctly for your team.
Beta Testing - The customization should now be installed in a test environment and multiple stakeholders should be allowed to test the customization. Sometimes by allowing multiple users on a piece of code they can expose weaknesses that you didn't know were there because they may use the system in un-expected ways or sequences.
Launch! - Once the customization has been through these steps it's time to install the code into your live system. We typically only install things on Tuesdays or Thursday's after hours. You will need to discuss with your partner on a time that makes sense for your operations to ensure little to no disruption to your users.