[geordief (OP)]

I have been scratching my head as to how an electron creates an electron field.

Then I recall that it  the electron is considered as an excitation of the electron  field.

Then I recall that the field is just a  number of measurements (made with electrons?)

So what is is that  produces the excitation in the field?

Do these excitations  produce their own fields  ?Do these fields  add together  constructively and can they cancel out like waves?

And are these fields all in relative motion?

[Kryptid]

Electrons, being an excitation of the electron field, don't create an electron field themselves. The excitations are produced by other particles interacting with the field and transferring some of their energy to it. A pair of high energy photons could interact with the electron (and positron) fields to transfer all of their energy into these fields. The result is an electron-positron pair. The energy transfer can only happen in a way that preserves the appropriate conservation laws.

[Halc]

A pair of high energy photons could interact with the electron (and positron) fields to transfer all of their energy into these fields.

If I read the literature correctly, these are different excitations of the same electron-positron field.

[Colin2B]

I have been scratching my head as to how an electron creates an electron field.

As @Kryptid says, the electron does not create the electron field

Then I recall that it  the electron is considered as an excitation of the electron  field.

Then I recall that the field is just a  number of measurements (made with electrons?)

To recap your recall, a field is a description of something we observe.
We can describe a wind field in which at any point in space a vector describes the strength and direction of the wind.
We can define a gravitational field such that at any point a vector describes the strength and direction of a force on a test mass - usually 1kg.
I suppose we could say that a tornado or a sea breeze are excitations of the wind field, or that a planet is an excitation of the gravitational field; but we don’t.
The way we describe an electron in QFT is by a Lagrangian and we use it to describe what we call the Dirac fermion in a fermion field - this also covers the positron. If you can follow the separate discussion on the Lagrangian then you are part way to understanding QFT. The Lagrangian is a useful way to describe a system because it is independent of coordinate transforms and it is very good at handling complex constraints.

So what is is that  produces the excitation in the field?

The electron; it is the excitation - also called a quantum of the field.
You need to separate the models we use from how you might interpret what they mean.
Lets take 2 examples.
In QM we describe the electron in a way that mathematically considers it to be anywhere in space. (That’s a bit like you being unable to find your keys and if asked you might say “they could be anywhere”. Well we know they aren’t ‘anywhere’ eg the moon so we narrow it down to where they are most likely to be eg your coat pocket.) This leads people to the interpretation that electrons can be anywhere in space and don’t have a position, but we know in reality that they are most probably very close to the nucleus of their atom and in fact the equations tell us that that is so (however, we don’t know where the electron is until we actually detect (measure) it). We also know that that form of QM is wrong, which is why we have QFT. In QFT the field operators have positions in spacetime so we can talk of electrons having positions.
However, both models have their uses and are valid in different circumstances, so if someone here says that an electron does not have a definite location and is spread out over all space we don’t question it, it is a valid mathematical model in some applications. However, that is not the same as believing or interpreting that the electrons in the screen you are looking at can suddenly appear at the other end of the universe - probability as close to zero as makes no difference.
Take care how you interpret the models.

Do these excitations  produce their own fields  ?Do these fields  add together  constructively and can they cancel out like waves?

Well, the electron does have an electric field* associated with it and electrons  can behave like waves and ‘interfere’. But beware, that interference is a description of the probability of the electron’s position when it hits a detector.
* in QFT this electric field is also part of the electromagnetic field which describes photons and is sometimes called the photon field. It is a moot point whether we can say the electron ‘produces’ an electric field, more correct to say an electric field is associated with it.

And are these fields all in relative motion?

In general no, but you could define coordinate systems where they do - should you want to.

[Kryptid]

A pair of high energy photons could interact with the electron (and positron) fields to transfer all of their energy into these fields.

If I read the literature correctly, these are different excitations of the same electron-positron field.

Oh, right. I believe positrons were supposed to be, what, holes in the Dirac sea? Or a time-reversed electron?

[Colin2B]

I believe positrons were supposed to be, what, holes in the Dirac sea? Or a time-reversed electron?

There have been a number of road bumps on the way to the current models 
Fortunately each one was a learning experience!
Again, @geordief  dangerous to take the maths too literally.

Added Note: it’s worth noting that the Dirac and Feynman theories are formally equivalent and can still be used today depending on the situation. Feynman’s work led to his famous diagrams.