No rules about kind, size, wording, or placement of signs. A sign doesn't even have to exist. On private property the owner of the property can simply tell you verbally that you can't carry, as can employees of a business. If this happens, then just leave, don't cause a scene about there being no sign because there is always the chance that others have visited there hundreds of times while concealing and no one has known. Once the sign is placed then all those other people are going to be S.O.L. if they return
There is one important point to make about signs and private property in Virginia.
While there are places that
are prohibited by statute, (schools, etc.) it is not a
statute violation in Virginia to carry on private property, in and of itself.
This is a little sticky, and obviously I can't give legal advice, but in general terms, Virginia is unlike some other states where violation of the property owner's wishes is actually a crime. Here, once you learn* that you are not welcome, simply leave. There are debates on signs, and fair notice, and blah blah blah, I'll leave it to those with cites at their fingertips to fill in the blanks. Generally speaking, especially if you didn't see a sign, you're fine until someone who has the authority to do so tells you to leave.
And of course once that point is clear, you comply immediately, leaving full carts of groceries or other hopefully expensive merchandise, behind for the next sucker to buy instead of you.
*One final thought... often people are ambiguous about asking you to leave. They might say "sir you can't have that here", or "sir, you need to leave that in your car"... I found one of the best pieces of advice I've heard here is to simply reply with "What are you asking me to do?" That puts them on the line to tell you exactly what they want. If it's to leave, then fine, you know, no ambiguity. If it's some mealy-mouthed rant about feelings, then that's fine too, you can safely ignore those.
TFred