A polarization maintaining (PM) fibre is one in which the two lowest modes have orthogonal linear polarizations. This is created by breaking the rotational symmetry of the index, as shown here:
So you can couple into just the horizontal mode, or just the vertical mode, or both. If you couple into both, then the output will be a coherent sum of two linear polizations, ie, elliptical in general. You might get (un)lucky, and see a linear polarization, if the phase is just right. But after a few minutes or hours, the temperature of the fibre may drift, and change the relative output phase of the two modes. Thus a previously linear phase will become circular.
In other words, a PM fibre can be thought of as a kind of variable phase wave plate. In the lab, we buy "zero order" quarter-wave and half-wave plates to make sure they are insensitive to temperature drift. A fibre is however about a million lambda long. I'm not sure what the absolute relative phase is, but it is empirically observed to be unstable.
So, how does one make sure the input is aligned to the mode axes?
Quick and dirty
First, pay attention to the "tab" in the connector. To within some spec, manufacturers align the slow axis of the fibre with the this tab. So make sure it is pointing along one of the axes of your polarizing beam splitter cube (PBSC), and that's a good starting point. But which axis? See this document for further discussion of what the "slow" and "fast" axes are, how they relate to the construction of the connector. Most likely, if you are taking the beam transmitted through a PBSC, then its polarization is vertical ("s"), and the key for the fibre should be in the horizontal plane (if it is aligned to the slow axis, which is standard). This is a good starting point.
However interference is unfortunately a homodyne effect. In other words, a 1% impure polarization, when drifting through all relative phases, can cause a 20% change in power. In applications where power stability is important, you need to do better.
So, here's how to know you have the input polarization aligned with the fibre axes:
1. Input: Set up polarized light into the fibre, through a half-wave plate.
2. Output: collimate, send through a half-wave plate, and then a PBSC. Put a photodiode after the PBSC. (You could also have a PBSC that rotates, there's one of these kicking around the lab.)
3. Measure the visibility of the output, but rotating the output half-wave plate. Visibility is (max-min)/(max+min). In the ideal setup, you would have the waveplate on a motorized rotation stage, since you want to monitor visibility for the next few steps.
4. Maximize the visibility by rotating the input half-wave plate.
5. Now you need to change the relative phase delay of the two fibre polarization modes. This can be done either by heating the fibre (holding it in your hand is sufficient) or by flexing/stressing it. Be careful not to damage the fibre, it has a minimum bending radius.
If in step 5, you see the visibility go down, then you're not aligned to the fibre axes. Go back to step 4. If the visibility is never robust against fibre phase change, then the input polarization may be impure, or your fibre may be multimode.
Dan's Quick and Dirty
Using the setup described above, with the photodiode measuring the power in the beam reflected by the PBS. First you want a good trace of the photodiode voltage, set the scope to have time per division on the order of seconds so that when you slowly and periodically perturb the fiber, tens of oscillations can be seen on the screen. Once you have the roughly aligned the input half-wave plate, adjust the output half-wave plate to give the largest possible photodiode voltage. Then while constantly perturbing the fiber, I recommend gently bending away from coupling optics, locally scan the angular position of the input half-wave plate. The optimum alignment will correspond to the largest photodiode signal that is least sensitive to perturbations. You will likely have to readjust the position of the output half-wave plate depending on how well the polarization is initially aligned.