The exact size of the capacitors is absolutely necessary for ensuring stability (unless you really know what you are doing). Unfortunately, the real world doesn't always work like AP Physics. The datasheet for your regulator will tell you what size capacitor and any other requirements like type (tantalum, ceramic, etc), locations, etc *.
The datasheet for the 7805/LM340 is available here:
http://www.national.com/ds.cgi/LM/LM340.pdf. If the part you get is not manufactured by national, you should get the datasheet from that manufacturer. There may be a few subtle differences (not likely for the 7805, but you'll probably run across a difference in some other chip before too long).
As far as heatsinks, it depends on how much current you plan to draw and the package of the regulator. Looking at the national datasheet, at 25 degrees C, the TO-220 can dissipate about 2 watts, although for safety, lets use 1 watt. The equation for power dissipation can be approximated by Pdis~=(Vin-Vout)*Iin. Since Vin is 12v and vout is 5v, you can solve for Iin of 1/7 of an amp. Since that's Iin, your output current (Iout) could actually be 350ma. I have a feeling that's more then enough for your application.
All of the grounds should be hooked together, the ground from your source, the ground from your regulator (middle pin of the TO-220 as well as the case), and the ground of whatever the load or loads are (IE your TTL chips and anything else).
Note that I've never designed a regulator circuit (other then a bridge rectifier), so you'll be a step ahead of me. I have worked with a bunch, though.
* I've seen a person with an EE degree and several years industry experience that designed a regulator circuit that didn't quite work because he didn't follow the requirements listed in the datasheet.