Lots of different ways to do it that typically involve the following:
(1) Identify starting universe.
(2) Source and process underlying attribute data for each holding (for instance, for a low vol factor, possibly ST and LT vol for each security).
(3) At this point, there is tons of variability. Once you have your factor data, some simply use it for selection (eg, pick top 200 based on low vol score) and use any variety of weighting schematics (market cap, equal-weighting, fundamental weighting, etc) thereafter.
Others, use the factor scores in some way to determine weighting and don't explicitly consider selection (eg, over/under-weight security relative to its benchmark weight based on its factor score--stocks with 'high' low vol scores get overweighted, 'low' get underweighted).
Still others use a combination. For instance, start with an equal-weighted portfolio and multiply by a normalized factor S score (0-1). Resulting weights are then scaled to sum to 1. Only securities with a factor score > 0 are kept, and weighting is a combination of EW with a factor tilt.
Beyond that, if you're able to go long/short, AQR creates fractiles based the factor scores, then goes long/short the top and bottom buckets. Various index providers create factor portfolios in the long-only space as well.
(4) Multi-factor portfolios represent another level of complexity as they include some or all of the above in combination with others (multiplicative, additive, blend, etc).
In short (or not), once you get past step 2, you can take it any number of ways and there isn't really a 'right' way to approach things. Once you have the data portion set up, probably best to just read some papers and do some testing on your own.