After 17 years on T-SQL I’m at last on my first project with Postgres. Here are the first things I needed for the transition:

• Do this first: https://wiki.postgresql.org/wiki/First_steps as it answers most of your first questions about connections, databases, using roles for logins, users and groups, and so on.
• 'String concatenation is done with ' || 'a double pipe '.
• No NVarchar is needed, just varchar. The default installation uses UTF-8. In fact the usual idiom is to use the text type, because omitting the length-specifier performs marginally better on postgres.
• Date & Time: use timestamp for datetime/datetime2
• Read https://www.postgresql.org/docs/9.1/static/datatype-datetime.html for more on dates, times and intervals.
• Use semicolon terminators nearly everywhere. If ... Then ... ; End If ; T-SQL doesn’t need them but Postgres demands them.
• plpgsql script is strictly separated from “pure” standard SQL in a way that T-SQL just doesn’t bother with. If you are writing scripts, plpgsql must either be inside a function or inside an ‘anonymous function block’. It is always delimited by $$ or $somestring$; and Declare variables in one block before Begin :

  Select 'This line is plain SQL' ;
  Do $$
  Declare
    anumber integer ;
    astring varchar(100);
  Begin
  If 1=1 Then
   Raise Notice 'This block is plpgsql' ;
  End If;
  End $$ ;
  Select 'This line is SQL again' ;
  

  In fact, Postgres functions are defined in a string. The $$…$$ delimiters is actually a postgres syntax for a literal string constant anywhere in code, in which you don’t have to escape any special characters at all. Functions can be defined in other languages than plpgsql. See e.g. https://pgxn.org/dist/plv8/doc/plv8.html.

• Variables: just use a plain identifier myvariablename with no @ symbol or other decoration. BUT as a consequence you must avoid variable names in a query that are the same as a column name in the same query. BUT BUT in Ado.Net Commands with Parameters, still use the @parametername syntax as you would for SQL Server
• Use Function not procedure:

  Create or Replace Function procedureName( forId int, newName varchar(20) )
  Returns int -- use returns void for no return
  As $$
  Declare 
    localvariable int;
    othervariable varchar(10);
  Begin
   Insert into mytable (id,name) values (forId, newName) On Conflict (id) Do Update Set Name=NewName ;
  End $$;

• Ooh, did you notice the ‘Create or Replace’ syntax, and how Postgres has a really good Upsert syntax – Insert On Conflict Update ?
• Postgres does function overloads, so to drop a function you must give the signature: Drop function functionname(int)
• Whereas the T-SQLer does everything in T-SQL, other database systems use non-sql commands for common tasks. For working at a command-line, learn about psql meta-commands.. Start with \c to change database, \l to list databases, \d to list relations, and \? to list other meta commands.
• Postgres have (I think) made more effort than MS to stay close to the SQL standards and as with T-SQL, the docs go into detail on deviations. But this means that much of your code for databases, schemas, users, tables, views, etc can be translated fairly quickly.
• Replace Identity with Serial or from Postgres 10 you can use the standard-but-wordy GENERATED BY DEFAULT AS IDENTITY. For more complex options, Postgres uses SQL sequences.
• Postgres replaces logins and database users and groups with a single concept: role. Permit a role to login with the With Login clause when you Create or Alter it: Create Role MyNameHere With Login. Grant it access to a database with Grant Connect: Grant Connect on Database dbname TO roleName. Make it a group with – well, it already is a group. Add other roles to it with Grant Role1 to Role2. I think this approach turns out to be much easier both to evolve and to understand and manage.
• The Nuget package for Ado.Net, including for .Net core, is Npgsql
• Scan these
  • Postgres SQL language
  • Postgres DataTypes
  • Postgres Server Admin

Converting T-SQL to Postgres

Here’s my initial search/replace list for converting existing code:

Authorization

Usually you will connect to postgres specifying a username. The psql.exe commandline tool will default it to your windows username. You can avoid passwords in scripts that use psql by putting them in the pgpass.conf file). If you want to set up integrated security, the limitation is that for computers not in a Domain it only works on localhost. The instructions at Postgres using Integrated Security on Windows take about 5 minutes for the localhost case, and include a link to the extra steps for the Domain case.