how to connect a AD9225ARS 12-Bit, 25 MSPS A/D Converter with arduino

Hmmm....then perhaps you just want an 8-bit ADC? I think tht would be a weird way to connect up the chip and probably risky. But then again, never hurts to try. The larger issue is that you will be getting data coming in at 25 MB/sec which is quite a load for a microcontroller. You'll need to figure out how to process data that quickly. You might need to burst it in, have some programmable logic to calculate an average, or just sample slower. Might also want to check out if you can use the internal ADC to prototype your design and then scale it faster from there. Most oscilloscopes with decent speeds use FPGA to interface the ADC since the data rates are so high.