Centers regularly provide flight following for VFR aircraft, as an additional service. It's a bit different from Terminal flight following, however.
You can contact us using the low IFR chart frequency, or look up an approach plate near where you are flying for a frequency.
We will normally want your aircraft ID, type, equipment qualifier, and destination, so we can enter a flight plan. If you are doing a round robin, a photo mission, or a sightseeing flight, it's handy for us to have a general idea of your intentions, which we use for briefings, and, if necessary, search and rescue.
We will provide traffic advisories and alerts, advise you of any special use airspace, TFRs, etc, that you may encounter, and can provide information regarding radar displayed weather, etc.
We can vector you around such items, upon pilot request. We usually only initiate vectors for TFRs or traffic. If you want a vector around an SUA or weather, let us know. If a vector will put you into IFR conditions, you'll also need to let us know.
Centers, however, may not be able to provide services if you are below radar/ADSB coverage, or out of frequency range. Also, we can terminate the service at any time. (We usually don't, unless it's radar, frequency, or workload related)