How to create an AR filter in Matlab
Answering in reverse order,

For a tutorial, I recommend: (the all pole case is an AR model)

J. Makhoul, "Linear prediction: A tutorial review," in Proceedings of the IEEE, vol. 63, no. 4, pp. 561-580, April 1975.

doi: 10.1109/PROC.1975.9792

Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals. The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal. In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum. The major part of the paper is devoted to all-pole models. The model parameters are obtained by a least squares analysis in the time domain. Two methods result, depending on whether the signal is assumed to be stationary or nonstationary. The same results are then derived in the frequency domain. The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra. This also leads to a discussion of the advantages and disadvantages of the least squares error criterion. A spectral interpretation is given to the normalized minimum prediction error. Applications of the normalized error are given, including the determination of an "optimal" number of poles. The use of linear prediction in data compression is reviewed. For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients. Finally, a brief introduction to pole-zero modeling is given.
keywords: {Control theory;Econometrics;Frequency domain analysis;Information analysis;Predictive models;Rhythm;Signal analysis;Statistics;Time series analysis;Tutorial},
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&amp;arnumber=1451722&amp;isnumber=31191

How does one get rid of an AR process?

The inverse filter to an all pole filter, is a FIR filter using the AR coefficients.  Inverse filtering is my guess of what that means.

Question one,
There are a number of AR estimators in Matlab's Signal Processing tool box. You can look at those, or read the above paper and roll your own.  Essentially, you have to estimate the covariance of adjacent pairs of samples, and then use one of the methods detailed in the paper.  The term "one tap" might be confusing, [1 a0] might correspond to one tap or two, but [1] doesn't make sense while [1 a0] does.