Welcome to /r/Tulpas. In this subreddit, you can discuss tulpas, share your experiences with making a tulpa, give advice to people making a new tulpa, or talk about things your tulpa said or did.
What is a tulpa?

While everyone has their own interpretation, a common definition of tulpa agreeable across our guides, FAQs and glossary:

A tulpa is believed to be an autonomous consciousness, existing within their creator’s mind, often with a form of their creator's initial choice and design.
A tulpa is entirely sentient and in control of their opinions, feelings, form and movement.
They are willingly created by people via a number of techniques to act as companions, muses, and advisers.

Put simply, a tulpa is a sentient imaginary friend. The key difference is that, unlike the classic idea of an imaginary friend, a tulpa does not do exactly what you want it to do. A tulpa possesses independent thought processes and forms its own opinions. This is generally taken as the mark of sentience in the tulpa community. That said, the definition of sentience is disputed and varies, both within the tulpa community and in general.

A tulpa, once created, can communicate with you at any time. They are almost always present in some form, even when idle or not paying attention. Communicating with a tulpa can be done vocally (obviously in a private place!) or mentally, simply directing your thoughts towards them and keeping your mind open. Responses may be as simple as an emotional impulse, a full coherent response (people often ascribe an ‘external’ or ‘alien’ quality to such responses), or even full auditory hallucination of speech. Initially, communication is quite limited, and it takes months of practice to improve. While some part of them remains ever-present, tulpa are typically responsive to their creator’s wishes and can divert their attention and communication if their creator is socializing with others or wishes to be alone.

One of the most common ways to experience and spend time with a tulpa is to visualize what they look like in what we call a “wonderland”, known by some as a dreamscape or mindscape, where you can hang out together. A wonderland is a just a persistent mental environment, easily recalled and visualized. Wonderlands are not strictly necessary though, however convenient or relaxing they may be.

Tulpa aren’t a replacement for human social contact, but a means of personal insight, improved perspective, and companionship outside of your usual social life. While some may seek to use a tulpa in lieu of a social life and a wonderland instead of experiencing reality, we don’t condone or encourage that, and if you try to anyway you’re likely to find your own mental schism admonishing you for such escapist behavior!

Ultimately, each tulpa is unique and distinct to the mind of their creator and host, so while we can assert generalities, specifying exactly the how and why of tulpa is beyond our current capabilities. We are seeking answers through collaboration and comparison though, and hopefully we’ll have shared some of our individual and collective insights and experiences though this subreddit and its wiki.

An older answer to the question, from one of the tulpa community's founders, can be read in FAQman's What is a tulpa?.