General: The key really is to be prepared ahead of time; if you need to forage for food, fuel, or weapons at the outset, you're already dead. The decision to bug-out depends on where you live, the physical patrticulars of your domicile, and how advanced the crisis is before you recognize the danger. Staying put may be the best thing to do (initially, at least), especially if civil unrest is already widespread, and is between you and your bug-out location. During Katrina, those who left New Orleans 24 hours prior to the storm reaching landfall were able to find gas along the way and moved at posted speedlimits. Those who waited until 12 hours prior found the interstates jammed and gas stations without gas (and many left home with near empty fuel tanks). Needless to say, the people in this second group did not fare well. Either way, stay away from government run shelters. The government wants you to gather there, but not because it's better for you; rather it's better for them, and we saw during Katrina how well that worked out.
You also can't count on the availability of any bug-out location that is not under your control prior to the disaster. Counting on a FEMA or national guard facility for either shelter or supplies is wishful thinking. If they're not occupied and protected when you get to them it's because there's nothing left worth stopping for (and risking you life for in clearing and searching them).
Preparation: Regardless of the nature of the disaster, you should have the following on hand at home...
1) One year of long-shelflife food, and the means to prepare it; also have as much water on hand as possible, and the means to purify more. I could write several paragraphs on just the latter, but the bottom line is, you can't have too much pottable water on hand.
2) A 72-Hour bug-out bag for each member of the household containing food, water, and basic survival gear. This should include a survival-type radio, to keep tabs on the goings-on in the world, and when it might be safe to return home. Also included is critical documentation such as passports and birth/wedding certificates, and any medication you need (as much as you can carry, but at least several weeks worth).
3) Weapons (both firearms and melee) that you are familiar with, and ammo for them; I prefer to be able to arm each family member with a long gun and a sidearm. Keep a bug-out ammo stash with your 72-hour kits, such that you have at least 100 rds for each calibre of weapon you plan on bugging out with.
4) And I can't stress this enough, either have sufficient gasoline on hand to top off your expected bug-out vehicle, or always insure you keep the tank full enough to drive to your bug-out location and back again.
Bug-Out Location: Again, any plan in this regard that counts on good luck (finding a hidden and uncontested FEMA bunker, a ferry or other boat you can seize, or someone else' mountain retreat you hope to find and occupy) is a plan for failure. If you don't have a place prepared ahead of time, than you are almost always better off staying put. In your own home, you have some supplies and measure of security. Being out in the open, with no absolute destination in mind, makes you just another one of the roaming refugees (fastfood for the zombie hoards). You should also have several evac routes to reach your bugout location, and have practiced the routes in daylight and at night.
Again, I could go on at length (was disaster prep NCO for my unit back in the service long ago), but you get the idea. There any number of excellent sources of info on meeting and surviving disasters. At the very minimum, anyone with a very modest investment of time and money can put their 72-hour kit together, and I recommend doing this immediately.