Without spending loads of money on expensive and fragile carbon parts, your best ways minimize weight are to
1. build your bike around an aluminum frame and carbon fork
2. stay away from boat anchor wheels. Deepvs, 32-36 straight gauge spokes, and track hubs are absurdly heavy. Go custom and use lighter rims (like an Open Pro or Niobium 30), use butted spokes, and use a road front hub or wheel with fewer spokes. (The road front hub alone will make a very big difference in total wheel weight)
3. use a 3/32" drive train
4. use road bars and stem (track bars and stem tend to be heavier)
5. stay away from Brooks saddles (good, light saddles can be found for cheap)
6. get a high quality aluminum seatpost (Thomson)
7. get folding tires (not wire bead)
8. Use clipless roadbike pedals rather than clips and straps.
9. Pay attention to the weight of the individual components. Reasonably light stuff can be found for cheap, but expensive stuff is not always the lightest. Small weight differences in individual components can really add up to a lot of weight savings.
10. Once you get the bike built up, you can continue to gradually reduce weight cheaply by tricking it out with small touches like ti stem bolts. However, you will soon reach a point of diminishing returns.

Building a light bike is a fun challenge, but just remember that its not really going to make you faster.