Disclaimer: Please be aware that this is the method I have developed for my own wood drying. Some species of wood may give off toxic fumes. Anyone who attempts to dry wood by this method is accepting the risk of fire associated with micro waving wood. Anyone who follows these recommendations accepts all responsibility for their actions.
Drying wood for small projects in a microwave is an effective means of reducing moisture content and preventing post-assembly shrinkage and gap widening in your intarsia projects. Air dried wood will shrink in a dry indoor environment and gaps will widen. A piece you thought was perfectly tight will reveal gaps over time.
The amount of time that the wood is "nuked" depends on the initial moisture content of the wood and the total volume of wood you are nuking.
Place about 3 board feet of wood in the microwave in a batch. The wood can be any number of pieces and any size from a few square inches to whatever will fit in the microwave. Just stack it up so it is about four boards (or layers) thick. It should all be about the same moisture content to begin with. You probably could mix green wood with air dried wood but I suspect you would be initially adding moisture to the drier wood.
Resinous woods will exude pitch from knots. Be careful of where they are placed in relation to the other wood in the stack. If the wood is green, begin by nuking it for 4 minutes on high. If it is air dried, nuke it for 2 1/2 to 3 minutes. Then take the wood out and pile it on a counter shingle fashion with just enough overlap so one end of each piece is supported up off the counter surface by the piece it is resting on. You will notice that the counter top under the pieces will condense moisture given off by the wood. Let the wood come back to room temperature and then repeat the nuking process. You may have to repeat the process 5, 6 or more times depending on how moist the wood was to start with. As the wood becomes drier, you will need to reduce the repeat nuking time in stages down to about 1 1/2 minutes.
If the initial amount of wood is less than 3 board feet, the nuking time will have to be reduced. You can judge the correct time by the temperature of the wood when you take it out of the microwave. If it is too hot to handle it is overheated and may split and/or burn. Reduce the nuking time by 30 seconds or more for the next treatment. You may have to experiment with nuking times depending on the amount of wood you are using and the wattage of your microwave. Higher wattage will heat the wood much faster.
As the wood becomes drier, the amount of moisture condensed on the counter top will diminish. Check under each piece after about 30 seconds. When only a small amount is condensed, that piece is generally dry enough. You probably don't want to reduce the moisture content below 7%. Wood that is too dry will absorb moisture and attempt to swell. In an assembled piece, this will create compression pressures that may cause the piece to virtually explode at the joints when the pressure becomes too great.
DO NOT attempt to dry it to "oven dry" since this is where you can cause it to start fire. The wood will burn from the inside of the piece first and may not even show any symptoms on the surface. Cutting it will reveal a black charred center. It will also give off smoke from the ends of the piece, although this can be confused with steam. It WILL catch fire if you over nuke it. Even if you don't have to call the fire department, your wife will definitely not appreciate the effects on her microwave! Pouring water on it will not immediately put it out since it is burning in the dry center. If you do manage to catch one on fire, toss it outside or immerse it in a sink full of water. It will continue to smoke for quite a while.
Small pieces and thin stock dry much quicker than larger pieces. The mass of the piece is the critical factor. Experience will teach you how long to nuke the wood and how dry to get it. The amount of moisture on the counter top and the "feel" of the wood are the best clues to dryness. If you have a moisture meter, that is the best measure.
This method was developed when I started making "tree cookie" coasters in 1990. Tree cookies are cut from main stems of small trees up to 6" diameter. I tried making them from branch wood, but there are too many internal tensions in this wood. The wood must be cut when the tree is dormant and not in its active growing season or the bark may not stay attached to the wood as it dries. In the northern states this is "winter wood". Some species will not retain the bark because it does not dry at the same rate as the wood. Properly dried, the cookie will not split like it would if it was air dried. After drying, the cookie should be sanded and finished.