What the self is not
The self is different from 'I' (or personality), which can be considered the sum of its identifications. The self (as the source of awareness and intent) already exists when an infant is born, while most of aspects of 'I' do not, but are slowly formed. The self initially identifies with that which enables the materials of awareness and can be influenced directly by intent. This is normally a physical body. That the self identifies with the body rather than being the body is implied by the fact that in dreams the self can dis-identify from the body and identify with an image (without even noticing the difference). The same applies to one's thoughts, behaviour, name, various roles, etc. They all constitute what is commonly referred to as 'I', but they are not part of the self, nor is the self part of them:
The self itself, the necessity - as Kant put it - of the ‘I think' being able to accompany all of my representations, a transcendental ego which is quite different to, and independent of, the empirical self that in the natural standpoint each of us identifies as 'me'. (Solomon, 1988, p.136)
So, any part of oneself that the person can observe, imagine or think of, is a part of 'I' not the self. For example, you can observe your thoughts, but this requires distancing from them, indicating that your self is different from your thoughts. If you have an image of the one who observes, this also can only be just another identification, not the self. Michael Daniels, a psychologist with a special interest in transpersonal psychology, explains this in the following way:
This mental-intellectual realisation of our own subjectivity occurs at the moment when I have the thought that I exist as an experiencing and active centre. It is, therefore, based on the simple ideas that 'I experience this and 'I do this. Such thinking immediately sets up a dualism between subject and object. Since I also realise that any ideas about myself are themselves objects to experience then 'I cannot be any thing I think I am. The real 'I' must, therefore, be the subject - the witness or agent who is distinct from any mental contents such as perceptions, thoughts, intentions or self-concepts. (2005, p.168)
In theory, the self can identify with an infinite number of forms. These identifications do not require a special type of connection, they are based on already existing connections. This is similar to a driver, for example, who identifies with the car s/he is driving (it often feels like a body extension while driving) or a person who identifies with a pair of glasses as long as s/he is wearing them.