A Recovery Model is property of a database that control how transaction log is maintained. SQL Server supports simple, FULL and BULK-LOGGED recovery models. There are multiple ways in which to check recovery model of a database in SQL Server.

1. Using SQL Server Management Studio:
Right click on database in Object explorer -> Go to Properties dialog box -> Options page -> Recovery model

2. Using Metadata function – DATABASEPROPERTYEX():
SELECT [RecoveryModel] = DATABASEPROPERTYEX('SqlAndMe','Recovery')
GO 

Result Set: 
RecoveryModel
SIMPLE 

3. Using catalog view – sys.databases:
SELECT [DatabaseName] = name,
       [RecoveryModel] = recovery_model_desc
FROM   sys.databases
GO  

Result Set:
DatabaseName   RecoveryModel
master         SIMPLE
tempdb         SIMPLE
model          FULL
msdb           SIMPLE
Pubs           SIMPLE
EuWindows      SIMPLE
TestDB         SIMPLE
ProductCatalog SIMPLE
ReportDemo     SIMPLE
ReportServer   FULL
ReportServerTempDB  SIMPLE

(11 row(s) affected)

Using sys.databases catalog view is easier as it returns information of all databases on server. Hope this tutorial works for you!