The process to install Jira can vary slightly depending on your environment. For example we do have guides on Installing Jira on Windows as well as Installing Jira on Linux
Generally the main installation is pretty straightforward. Since you will have one environment using the MySQL database, you should be aware that this database use requires you to manually download and install the mysql jdbc driver .jar file into the $JIRAINSTALL/lib/ folder. Otherwise Jira won't be able to connect to a mysql database.
I would recommend following the Connecting Jira to MySQL guide (this guide includes the note about the jdbc driver download required as well) and for the other environment the Connecting Jira to MS SQL 2014 guide.
It is important to make sure that you create these databases per the steps in those guides. One step that frequently trips up first time Jira installers is that they do not create the databases with the correct collations as stated in those guides and as a result Jira tends to throw warnings about data integrity as a result. I would also recommend checking out the Supported Platforms documentation in order to make sure that your system is using supported versions of Java, database, browsers, etc that correspond to the version of Jira you plan to install.
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
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