Hi Vo Quang Hoa,

Please follow below steps 
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1.First login to Appexchange with your main account (ie. not sandbox).
2.Find the app you want to install in sandbox and click the "Get it now"
3.You will be asked if you want to install the app in Production or Sandbox
4.Choose sandbox and you will be automatically redirected to the test.salesforce.com
5.Enter in your salesforce sandbox credentials
6.Now just follow on screen instructions.
 

Difference between Test environment and Developer Edition
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A test environment for salesforce.com is crucial to change control. Salesforce.com provides the tools needed to test anything in a test environment before you implement it in your live instance. You can either test in a Sandbox environment or in a Developer environment. What is the difference? I will share what I know…
Sandbox
The salesforce.com Sandbox environment is an exact copy of your salesforce.com instance. You can copy your live instance to a sandbox environment (but you have to perform manually from sandbox to developer edition) where you can test any changes, implementations, AppExchange apps or updates. It can also be your hands-on training environment without risking your live data.
You can either copy your configuration and data into a sandbox environment or just the configuration. It acts exactly like your live instance, but be careful if you have workflow rules or automations because they will work in the sandbox as well.
I know that this sounds wonderful and if you don’t have it, you are dying to know how to get it. The problem is the cost. If you are on Unlimited Edition, then cost is not a problem because it comes included. But for Enterprise, Professional or Group Editions, you have to pay… and the price is hefty; anywhere between 25k-50k per year. For a lot of companies, that is more than they are paying for their live salesforce.com instance. So how do you test salesforce.com without Sandbox?  It is always suggested to develop application in sandbox instance then go for LIVE.
Developer Edition
Developer Edition was an edition created for development of integrations and apps, specifically for theAppExchange. It is also a great tool for testing/training in salesforce.com. What makes this a great tool is the fact that it is free. Anyone can get a Developer Edition of salesforce.com. It is a standard Enterprise Edition with very limited storage space. You cannot copy your configuration or data onto the Developer Edition, but you can customize it to match your instance’s look and feel. Once it is customized, you can use it for training, testing or anything else you want. It takes a little bit of work, but you can make it act and feel just like your live instance. The work is well worth it for the free price.
To get a copy of Developer Edition for yourself or your company go here. Play around with it. Get apps from the AppExchange. Do anything and everything that you have been scared to do your live system. 



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Thanks and Regards
sandhya