To answer this, I'm going to take a bit of an in-depth look at 18.2-119, because it is the most applicable to what you would likely be charged with. However, because of the similar wording, most of the analysis would seem to apply to the other sections skidmark posted.
18.2-119 states:
§ 18.2-119. Trespass after having been forbidden to do so; penalties.
If any person without authority of law goes upon or remains upon the lands, buildings or premises of another, or any portion or area thereof, after having been forbidden to do so, either orally or in writing, by the owner, lessee, custodian, or the agent of any such person, or other person lawfully in charge thereof, or after having been forbidden to do so by a sign or signs posted by or at the direction of such persons or the agent of any such person or by the holder of any easement or other right-of-way authorized by the instrument creating such interest to post such signs on such lands, structures, premises or portion or area thereof at a place or places where it or they may be reasonably seen, or if any person, whether he is the owner, tenant or otherwise entitled to the use of such land, building or premises, goes upon, or remains upon such land, building or premises after having been prohibited from doing so by a court of competent jurisdiction by an order issued pursuant to §§ 16.1-253, 16.1-253.1, 16.1-253.4, 16.1-278.2 through 16.1-278.6, 16.1-278.8, 16.1-278.14, 16.1-278.15, 16.1-279.1, 19.2-152.8, 19.2-152.9 or § 19.2-152.10 or an ex parte order issued pursuant to § 20-103, and after having been served with such order, he shall be guilty of a Class 1 misdemeanor. This section shall not be construed to affect in any way the provisions of §§ 18.2-132 through 18.2-136.
Let's break it down.
1) The phrase "without authority of law" means that it doesn't apply to law enforcement or other government officials (health/code inspectors, etc) on official business.
2) The phrase "goes upon or remains upon the lands, buildings or premises of another, or any portion or area thereof" means that either entering the property or remaining on the property are covered. This is important later.
3) The phrase "after having been forbidden to do so" makes it clear that you need to be notified in some way that you are forbidden.
Those are the key elements of the law. The rest of the law provides information on how you have to be notified, and essentially lists four different ways:
A) Orally (as in you are told not to enter or leave)
B) In writing (as in you have previously been asked by means such as a letter, handbill, etc)
C) By a sign that is posted where it may be "reasonably seen"
D) By a court order, under certain circumstances
A lot of the text is spent on who has the authority to issue the prohibitions in A-C, but in general we can summarize it as someone who either has the right to control the property, or is acting on behalf of someone with that right.
The code ends by stating that it is a Class 1 misdemeanor, which then provides the basis for what the penalties could be.
Now, in order to be found guilty of the crime of Trespass, the prosecutor has to establish all of the elements of the crime, as well as show that any exceptions do not apply to you. In other words, all he has to show is that you entered or remained on the property and that you were forbidden to do so by one of the methods listed above. If methods A, B, or D were used, it is usually fairly easy to prove it (such as by calling the person who issued the oral or written request to testify, or by presenting the record of the court order). Method C has a little more wiggle room. (For example, a 12-inch sign saying "No Guns" on every door can almost definitely be "reasonably seen", but a single line in fine print on a wall off to one side of one entrance is far less "reasonably seen".)
Because of this, most places (and even most police responding to a trespassing call) will issue a verbal or written warning to someone before they will have the person arrested. However, that simply makes the job of convicting easier. It doesn't mean that you can simply ignore a sign that you have seen. If you've seen the sign, then you have been forbidden to enter in writing by one having authority to do so. You might not be caught doing it, but that doesn't mean that you aren't violating the law.