Integration can mean many things.

Each of these is possible:

Data:

• Easy - shared files in folders - ftp, csv, scripts to move files and import/export files

• Harder - ETL (Extract, transform and load) which is more automated

Database:

• Easy - via JDBC or SQL for example

• Harder - via libpq/lua, Perl, Python, TCL, and PL/pgSQL over PostgreSQL to programmatically interact with tables and/or create and access stored procedures

Note: Database level integration is only available with on premise deployments.

Application: 

• Easy - via XML-RPC or JSON-RPC webservices or scripts - supports data and process integration

• Harder - intra-communication (ESB notifications/mediation/asynchronous) or inter-communication (Integration Platform - such as Babelway, Cleo, Adeptia,etc and SOA/EAI front end/federation/synchronous ) or connectors (Zapier, Microsoft Flow, Tray.io, etc) - supports data and process integration

The quickest is "easy data" integration - you use CSV or XLS files to move data into Odoo from other systems, leveraging the External ID if you plan to update that data (or import more than once) - more at https://www.odoo.com/documentation/user/14.0/general/base_import/import_faq.html

The most popular is "easy application" using the Odoo Webservice API's - https://www.odoo.com/documentation/14.0/webservices/odoo.html

This Odoo Webservice API's allow you to access every part of Odoo, including custom fields and methods in custom developed modules.  It is the same API that Odoo used to create the Web based User Experience - and you can actually see the API calls being made when a User is using Odoo by leveraging the Odoo log file options (log-request and log-response) - more at https://www.odoo.com/documentation/14.0/reference/cmdline.html#logging

There are also Python libraries (API wrappers) that have been developed:

https://github.com/odoo/odoo-client-lib

The Odoo Community Association has also developed a Python and REST API:

https://github.com/OCA/odoorpc

https://github.com/OCA/rest-framework