1. Open SQL Server Management Studio
2. Connect to the database engine for which you need the port number
3. Run the below query against the database

select distinct local_net_address, local_tcp_port from sys.dm_exec_connections where local_net_address is not null

The above query shows the local IP as well as the listening Port number

1. Open Run in your system.
2. Type %windir%\System32\cliconfg.exe
3. Click on ok button then check that the "TCP/IP Network Protocol Default Value Setup" pop-up is open.
4. Highlight TCP/IP under the Enabled protocols window.
5. Click the Properties button.
6. Enter the new port number, then click OK.

You can also use this query

USE MASTER GO xp_readerrorlog 0, 1, N'Server is listening on' GO

Source : sqlauthority blog

Visually you can open "SQL Server Configuration Manager" and check properties of "Network Configuration":

This query works for me:

SELECT DISTINCT 
    local_tcp_port 
FROM sys.dm_exec_connections 
WHERE local_tcp_port IS NOT NULL

To check all the applications listening on all ports, there is command:

netstat -ntpl

PowerShell solution that shows all of the instances on the host as well as their incoming traffic addresses. The second bit might be helpful if all you know is the DNS:

ForEach ($SQL_Proc in Get-Process | Select-Object -Property ProcessName, Id | Where-Object {$_.ProcessName -like "*SQL*"})
{
    Get-NetTCPConnection | `
     Where-Object {$_.OwningProcess -eq $SQL_Proc.id} | `
      Select-Object -Property `
                                @{Label ="Process_Name";e={$SQL_Proc.ProcessName}}, `
                                @{Label ="Local_Address";e={$_.LocalAddress + ":" + $_.LocalPort }},  `
                                @{Label ="Remote_Address";e={$_.RemoteAddress + ":" + $_.RemotePort}}, State | `
      Format-Table
}