(This is the non-illustrated version, pictures will follow as soon as I'm finished moving. Maybe.)
Vias are essential part of multilayer designs. For homebrew PCBs, vias are normally not through-plated, which means that you need to run a wire through the via and solder it on both sides, to create an electrical connection. This almost always creates a little bump of solder on both ends of the via. The consequence of this is that placeing vias under SMD ICs is a no-no, because the bump of solder would to big to allow the IC to be mounted. Not being able to use vias under ICs is unfortunate, because that is often the place where vias are very useful.
I have discovered a method which allows for vias under ICs. The only catch to this is that the via cannot be under two ICs at the same time, but for most designs this is not a problem. The trick is to make the connection directly under the IC as flat as possible. The way I do this is as follows:
First find a piece of wire that consists of silver coloured strands, like the following:
The reason for wanting silver coloured strands is because they are directly solderable. Most copper coloured strands, on the other hand, are not directly solderable because they are usually coated with a layer of some sort. To be able so solder those wires, one first has to remove the coating. This is not the case with silver coloured wires.
Next strip away a part of the wire and cut it into pieces of about 2cm in length. As the wire is cut, the individual strands will fall on the table.
Then take two strands and twist them around each other and then fold them into a fishlike shape. The shape is important because it prevents the wire from falling through; it acts as a gentle wedge. This is an essential part of the trick to getting a flat via connection.
Now stick the open end of the wire into the via, while looking onto the layer of the PCB on which the IC will be placed. So if the IC were to be placed on the top layer, one would stick the wire in from the top side.
Next push the wire through the hole until it is exactly flush with the board. Do not push it in any further, lest you will not be able to solder the wire to the via's edge.
Now gently apply some flux to the top edge of the via and solder it. Take care to use as little solder as possible so that you minimize the size of the solder bump on the top side. This is of course the goal of this whole excersize. It can be a bit tricky to do at first.
Next turn the board around and use some tweezers to try and gently pull the wire out. If you succeed in pulling out the wire, then the wire was not properly soldered and you are lucky that you discovered this now, rather than after having mounted the entire board. You will have to try again, usually using a new wire because the old one is dirty or doesn't stay stuck in the hole.
If the wire doesn't come loose, then you can safely solder the other side aswel. The other side doesn't need to be flat. After that, cut the remaining wire that protrudes from the via. After you have done all your vias, you might want to check all the connections with a multimeter, to be sure that the top part of the via is indeed electrically connected to the bottom part.