How exactly to implement the fractional part of a 'fractional equalizer'? I have written my own LSE equalizer (that works on the bit level), and literature I have read says that 'fractional' based ones are much better. So how exactly does one get 'fractional' bits? Is it as simple as resampling the softbit decisions to 2x, 4x or whatever of their bit rate and applying the equalizer like that?

Thanks
A typical ("non-fractional") equalizer operates at the symbol rate. That is, the inputs that you apply to the equalizer are generally soft decisions on what the unequalized received symbols are. A linear equalizer then takes this stream of soft symbol metrics and applies a linear filter that (hopefully) corrects for any non-ideal frequency response found in the path from modulator to demodulator.

The only difference with a fractionally-spaced equalizer (FSE) is the sample rate that it runs at: instead of the one sample per symbol that you see with a "standard" equalizer, an FSE operates at some multiple of the symbol rate. Typical values I've seen before are $T/2$- and $T/4$-spaced equalizers, which operate at twice and four times the symbol rate, respectively. 

These samples should be straightforward to obtain; whatever processing steps in your system are used to generate the symbol decisions (e.g. when obtaining symbol timing synchronization) almost certainly operate at a minimum of 2 samples per symbol. Instead of decimating the receiver output to one sample per symbol, keep the higher sample rate intact through the equalizer in that case.