When learning SQL (or any other programming language) it is not sufficient to read books or listen to lectures. It's absolutely necessary that one does exercises - prescribed exercises as well as own made-up tests. In the case of SQL one needs access to a DBMS installation, where he can create tables, store, retrieve and delete data, and so on.
This page offers hints and links to some popular DBMS. In most cases one can download the system for test purposes or use a free community edition. Some of them offer an online version so that there is no need for any local installation. Instead such systems can be used in the cloud.
Often, but not always, a DBMS consists of more that the pure database engine. In order to be able to easily formulate SQL commands, we additionally need an interactive access to the database engine. This is provided by different client programs and IDEs. They offer such an interactive access - and they are part of the downloads. (In some cases there are several different clients from the same producer.) At the same time there are client programs and IDEs from other companies or organizations which offers only an interactive access but no DBMS. Such clients often support a lot of different DBMS.
Derby
Firebird
IBM DB2
IBM Informix
MariaDB
MS SQL Server
http://www.microsoft.com/en/server-cloud/products/sql-server/default.aspx
MySQL
DBMS: http://dev.mysql.com/downloads/
IDE for administration and SQL-tests: http://dev.mysql.com/downloads/workbench/
Oracle
The Oracle database engine is available in 4 editions: Enterprise Edition (EE), Standard Edition (SE), Standard Edition One (SE One) and Express Edition (XE). The last-mentioned is the community edition and is sufficient for the purpose of this course. http://www.oracle.com/technetwork/database/enterprise-edition/downloads/index.html.
SQL-Developer is an IDE with an Eclipse-like look-and-feel and offers access to the database engine. http://www.oracle.com/technetwork/developer-tools/sql-developer/overview/
In the context of Oracles application builder APEX (APplication EXpress) there is a cloud solution consisting of a database engine plus APEX. https://apex.oracle.com/. Among a lot of other things it offers an SQL workshop where everybody can execute his own SQL commands for testing purpose. On the other hand APEX can be downloaded separately and installed into any of the above editions with the exception of the Express Edition.
PostgreSQL
SQLite
Online Access
SQL Fiddle offers an online access to following implementations:
MySQL, PostgreSQL, MS SQL Server, Oracle, and SQLite.