Psql could not connect to server: No such file or directory, 5432 error?

I’ve had this same issue, related to the configuration of my pg_hba.conf file (located in /etc/postgresql/9.6/main). Please note that 9.6 is the postgresql version I am using.
The error itself is related to a misconfiguration of postgresql, which causes the server to crash before it starts.
I would suggest following these instructions:

Certify that postgresql service is running, using sudo service postgresql start
Run pg_lsclusters from your terminal
Check what is the cluster you are running, the output should be something like:
Version – Cluster Port Status Owner Data directory
9.6 ——- main — 5432 online postgres /var/lib/postgresql/9.6/main

Disregard the ‘—‘ signs, as they are being used there only for alignment.
The important information are the version and the cluster. You can also check whether the server is running or not in the status column.

Copy the info from the version and the cluster, and use like so:
pg_ctlcluster start, so in my case, using version 9.6 and cluster ‘main’, it would be pg_ctlcluster 9.6 main start
If something is wrong, then postgresql will generate a log, that can be accessed on /var/log/postgresql/postgresql--main.log, so in my case, the full command would be sudo nano /var/log/postgresql/postgresql-9.6-main.log.
The output should show what is the error.

2017-07-13 16:53:04 BRT [32176-1] LOG: invalid authentication method “all”
2017-07-13 16:53:04 BRT [32176-2] CONTEXT: line 90 of configuration file “/etc/postgresql/9.5/main/pg_hba.conf”
2017-07-13 16:53:04 BRT [32176-3] FATAL: could not load pg_hba.conf

Fix the errors and restart postgresql service through sudo service postgresql restart and it should be fine.

I have searched a lot to find this, credit goes to this post.
Best of luck!

I had the same issue but non of the answers here helped.
How I fixed it (mac)

Try to start postgresql with pg_ctl -D /usr/local/var/postgres start
Look for the Error Message that says something like FATAL: could not open directory “pg_tblspc”: No such file or directory.
Create that missing directory mkdir /usr/local/var/postgres/pg_tblspc
Repeat from step one until you created all missing directories
When done and then trying to start postgresql again it might say FATAL: lock file “postmaster.pid” already exists
Delete postmaster.pid: rm /usr/local/var/postgres/postmaster.pid
Start postgres with: pg_ctl -D /usr/local/var/postgres start
Done ✨