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If you use Libpq binding for respective language, according to its documentation URI is formed as follows:

postgresql://[user[:password]@][netloc][:port][/dbname][?param1=value1&...]
Here are examples from same document
postgresql://
postgresql://localhost
postgresql://localhost:5432
postgresql://localhost/mydb
postgresql://user@localhost
postgresql://user:secret@localhost
postgresql://other@localhost/otherdb?connect_timeout=10&application_name=myapp
postgresql://localhost/mydb?user=other&password=secret
                If you still have problems, check the special characters in your password, change it temporarily for only numbers and test the URL (just to validate that your connection is working as expected)
– Edenshaw
                Feb 21, 2019 at 16:29
                My issue was to simply copying the "jdbc:postgres:// ..." string out of DataGrip. Unfortunately the error message did not help. Thank you!
– barfoos
                Jun 13, 2019 at 18:07
                To add to @Edenshaw's note on special characters, the password needs to be url encoded, I just stumbled upon this problem with a password containing the '@' character (replacing it with %40 solved it)
– Tom Hemmes
                Jun 30, 2020 at 11:28
                @RyuS.   The URI scheme designator can be either postgresql:// or postgres://  From here: postgresql.org/docs/current/libpq-connect.html#LIBPQ-CONNSTRING
– Grant Oberhauser
                Jun 26, 2021 at 21:13
Here is the documentation for JDBC, the general URL is "jdbc:postgresql://host:port/database"
Chapter 3 here documents the ADO.NET connection string,
the general connection string is Server=host;Port=5432;User Id=username;Password=secret;Database=databasename;
PHP documentation us here, the general connection string is
host=hostname port=5432 dbname=databasename user=username password=secret
If you're using something else, you'll have to tell us.
                Thanks. The ADO.NET format is also what you need to pass to UseNpgsql() for Entity Framework Core.  I was a little confused whether it should be that or the postgres:// URL (which I've also seen as "postgresql://")
– CrazyPyro
                Oct 21, 2020 at 12:44
                libpq (offical postgresql client lib)  understands both URL form and name=value pairs form. if you connection is not ultimately through libpq then consult the documentation for your framework.
– Jasen
                Nov 30, 2021 at 20:59
syntax:

"Server=host ipaddress;Port=5432;Database=dbname;User Id=userid;Password=password;
example:
"Server=192.168.1.163;Port=5432;Database=postgres;User Id=postgres;Password=root;
The connection string can also be retrieved programmatically from working DB connectors.
For instance I sometimes extract connection strings from SQLAlchemy's engine, like this:
> db_engine.url
postgres://{user}:{password}@{host}:{port}/{db_name}?sslmode=require
The general format of database url
DATABASE_URL=postgresql://username:password@host:port/dtabase_name
If you are using postgresql sql with asyncpg the database url would be
DATABASE_URL=postgresql+asyncpg://username:password@host:port/dtabase_name
Remember to never push your  database password so you should use your DATABASE_URL in .env file 

The port is optional if you use the default one
Like this you can connect both local and remote database think of that once you want to check an issue that occur in the remote deployed versions
ex of localhost DATABASE_URL would be
DATABASE_URL=postgresql+asyncpg://postgres:dina@localhost/mysens
If you deployed your database on Heroku and you want to connect it with your local app, go to Heroku Postgres installed add-on go to settings and click on view credential in Database Credentials and use the uri to connect to your database
DATABASE_URL=postgresql+asyncpg://sqnalxxxxxxxxx:160xxxx2bdd2942b26c93c392xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx@ec2-35-173-91-114.compute-1.amazonaws.com:5432/del6o4cjoqfsov
Some people seem to misread the database name as a server name and the host as a postgresql server? A host hosts a postgresql server that has a database. Or am I missing something.
postgresql://my_host/&server=my_postgresql_server?user=my_user&port=my_port&password=my_password&database=my_database
Example:
my_host: can be "localhost" (but that is not in the question) or an ip address of a host.
postgresql://my_host/&server=postgres?user=postgres&port=5432&password=postgres&database=test_db
Worked for me in Python with sqlalchemy and a postgresql localhost running. Needs sqlalchemy, postgresql, and psycopg2 to get it to work.
PS: The question is about a postgres://... URL, but this would not work here. Instead, you need postgresql, and what is run in the end in Python is dialect+driver (see Database URLs) = postgresql+psycopg2, without having to write it like this.
        
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