How do I specify that a column should be auto-incremented in pgAdmin?

two options: Use the "datatype" SERIAL or create a sequence and use this sequence as a default value for your integer:

CREATE SEQUENCE your_seq;
CREATE TABLE foo(
  id int default nextval('your_seq'::regclass),
  other_column TEXT
);
INSERT INTO foo(other_column) VALUES ('bar') RETURNING *;

If you want to do this in PGAdmin, it is much easier than using the command line. It seems in PostgreSQL, to add a auto increment to a column, we first need to create a auto increment sequence and add it to the required column. I did like this.

1) Firstly you need to make sure there is a primary key for your table. Also keep the data type of the primary key in bigint or smallint. (I used bigint, could not find a datatype called serial as mentioned in other answers elsewhere)

2)Then add a sequence by right clicking on sequence-> add new sequence. If there is no data in the table, leave the sequence as it is, don't make any changes. Just save it. If there is existing data, add the last or highest value in the primary key column to the Current value in Definitions tab as shown below.

3)Finally, add the line nextval('your_sequence_name'::regclass) to the Default value in your primary key as shown below.

Make sure the sequence name is correct here. This is all and auto increment should work.

This is pretty easy in pgAdmin 4.

First, add a column to your table, then click the little edit icon:

Then go to Constraints and select the Identity type:

Save your table and the column will auto-increment.