DE1: How to measure power consumption?

If you check the DE1 schematics thorougly, you'll notice that it has 0-ohm-jumpers for VCCINT and VCCIO. They can be replaced by low-ohm (0.1 ohm maximum) shunt resistors and allow a precise measurement.

A dynamical measurement as dicussed previously discussed could be done only at a slow (e. g. ms) time scale, cause high capacitance decoupling capacitors are connected directly to the power planes. A undistorted dynamic measurement of FPGA supply currents is basically impossible on a regular board, to my opinion. I also think, that the dynamic effects of fast currents transients (ground and supply bounce) can be better observed indirectly at I/O pins.