In your Magento admin, go to System -> Paypal. Check to see if "Sandbox mode" is activated in the Payment System you are using.
You can set up Magento and Paypal to work fairly seamlessly together. The easiest is probably to use the Paypal API. Log into your Paypal account and obtain the API username, password and signature, then just copy & paste those into the corresponding fields in the Magento admin.
You can test this by setting up a developer account in Paypal Sandbox. It is a bit difficult to get used to at first, but basically the steps are as follows:
- Create a Seller test account. This is a simulated merchant account that will act as the payment receiver.
- Create a Buyer test account. This is the simulated customer account that you will use to make test purchases in your store.
Note that you have to create email addresses for each of these accounts. They do not correspond to any real email accounts, and the mail you receive in these is always checked from within the Paypal Sandbox.
Once you have these test accounts, you sign into them from within the Paypal Sandbox. So you would sign into your test Seller account, get the API data mentioned above, and paste it into your Magento admin. (Be sure to set Sandbox mode to "true" in Magento when you are trying this).
In order to be able to make test purchases, you have to be signed into the Paypal Sandbox and have it open in the browser. Note that nobody else will be able to make actual orders through Paypal while you are in Sandbox mode.
You can then go to the public area of your store and purchases using the test Buyer account. If everything goes well, you will be able to see your fake orders placed and registred in the Magento admin area.
As a final note, I recommend having a preproduction version of your store for doing this kind of testing. This means setting up an exact copy of your Magento store (with a recent copy of the database) on another domain and activating it when you are doing testing.