I'm a big fan of Sketchup. I find its capabilities are limitless.
When I first started out, I believe I went about my drawings the wrong way and I'm guessing most Sketchup users start this way as well. If I was drawing a dresser, for example, I would make a rectangle the depth and width of the piece and then pull it up to the height. I would add the trim and hardware by pulling and pushing the shape I made. Then I would make doors and/or drawer fronts the same way and stick them on the piece. I might have used a few groups but with a big, hollow blob of a shape, groups and components aren't really necessary. This made making changes ridiculously hard and I would usually mess something up.
Now, I do my drawings just like I do woodworking. I make each piece individually. So start with small rectangular shapes that look like 1x4's, or whatever wood you're working with. Add your rabbets, half laps, dados, grooves, profiles, etc to each piece. Make each shape in Sketchup something that reflects an actual piece of wood that will be in the project. For example, if you have trim that goes around the top of the dresser, make it out of three mitered pieces, not one big U shaped piece. Make your rails, stiles and panels individually. It will take you longer up front, even when you get proficient at it, but it will save time when it comes to changes later. It also helps to visualize the construction process as you go through it.
Good luck and have fun,
I'm pretty sure Shakespeare would have traded his quill for a computer if they were available.