Can I dismantle a table to recover (some of) its wood?

I'm playing my first-ever game of Dwarf Fortress and chose to embark in a relatively calm area of the word, even though it's only sparsely forested.

Being a Minecraft player as well, I overestimated the reforestation rate and burned through a fair amount of my now-precious wood making tables for my dining hall before realizing I could make them out of stone instead. Now, I have no wood with which to make more beds, chairs, and so forth. (My first Fun!)

Is there any way to dismantle these tables so that I can make a few vital wooden supplies to tide me over until the saplings grow?

No, you can't get wood from your tables. A couple of other solutions:

• You can dismantle your starting wagon for three wood.
• You can buy wood from the elven and human caravans.
• You can dig down until you hit a cave with underground trees.

As stated, you cannot. To build upon the other answers, though, I'll add that caravans will bring a lot more wood if you have no wood in stockpiles. So if you plan on saving a lot of wood for later, don't expect caravans to bring hardly any, but if you have literally no wood logs, you can expect quite a bit. And as far as the trees regrowing, be sure your dwarfs aren't trampling the saplings on the ground. You can do this using walls or, preferably, traffic areas.

No. When you deconstruct furniture, all you do is unlock it from its position on the floor (or wall); it remains as-is.

Almost everything /except/ beds can be made out of non-wood substances -- thrones instead of chairs, rock pots (craftsdwarf's table) instead of barrels, and so on. If you're in a wood-poor area, use wood only very sparingly and only for beds, at least until you can talk to the outpost liason and offer him your dorfs' firstborn children if need be as long as the next caravan brings plenty of wood.

As to caravans, buy all barrels and bins you are offered and dump the contents if that's what it takes.

Do lots of exploratory digging in search of bituminous coal or lignite so you can use something other than charcoal to power your furnaces while you look for the magma pools.

Finally, when cutting wood, make sure not to cut down /all/ the trees in an area - leave some to drop seedlings for new trees a year or so down the line, and make sure not to trample them.