From: https://blogs.msdn.microsoft.com/steverac/2010/12/13/test-remote-sql-connectivity-easily/

Just go anywhere on your system and create an empty text file named anything but instead of txt 
make sure the extension is UDL.  Then, double-click on the file and up pops a SQL connectivity 
window to allow testing of remote SQL connections.

From: http://www.diaryofaninja.com/blog/2013/11/18/testing-connectivity-to-microsoft-sql-server-without-any-tools-installed

From: https://blogs.msdn.microsoft.com/docast/2014/10/24/tips-and-tricks-to-fix-sql-connectivity-issues/

Explained a few common scenarios;
Approached these connectivity issues; and
Included fixes for these issues.

From: http://www.jameswiseman.com/blog/2012/02/22/hiding-and-showing-a-sql-instance-network/

SQL Server Properties
In Management Studio, click on the server root, and select properties.
From the resulting dialog, select the ‘Connections’ page.
Ensure the checkbox “Allow remote connections to this server” is checked.
SQL Server Configuration
Run SQL Server Configuration Manager (located in within the SQL shortcuts under the windows start menu)
Navigate to “SQL Server Network Configuration” and then “Protocols for SQL2008R2”
Ensure TCP/IP is “Enabled”
Right-click on “Protocols for SQL2008R2” and select “Properties”
Ensure “Hide Instance” is set to “no”
 SQL Browser Service
Navigate to the Service Control Manager through control panel (or run “Services.msc”)
Ensure the “SQL Server Browser” service is started. (It may be best to have the Startup Type as “Automatic”

From: https://docs.microsoft.com/en-us/sql/relational-databases/backup-restore/create-a-full-database-backup-sql-server

A. Full local backup
The following example creates a full database backup of the MyDB database to the default backup location of the server instance Computer\Instance. Optionally, this example specifies -BackupAction Database.
PowerShell

Copy
Backup-SqlDatabase -ServerInstance Computer\Instance -Database MyDB -BackupAction Database  

From: https://msdn.microsoft.com/en-us/library/ms175477.aspx

This topic introduces the SQL Server backup component. Backing up your SQL Server database is 
essential for protecting your data. This discussion covers backup types, and backup restrictions. 
The topic also introduces SQL Server backup devices and backup media.