I had used two different ways to connect aspirators to the water source, usually a kitchen faucet. Both worked OK.
Right now, I have connected about four to five connectors to connect from garden hose size down to the aspirator thread size, I think that one is 3/8. But I had trouble finding everything that I needed, indeed I got everything OTC from hardware stores.
Probably easieast way is to remove aerator from faucet, screw in a garden hose adaptor, you can find it from waterbed filling kits, white plastic, it screws in the faucet. Now buy a copper ( maybe it is brass, I am not sure ) piece, it screws in the garden hose adapter one side, the other side has a male connector where you can push in a piece of garden hose plastic tube. Don't need to buy a garden hose for that, just buy a piece of plastic tube that fits in the metal piece and also in your aspirator, over the threads. Everything should be tight. Next buy small clamps and clamp the plastic tube to the aspirator and to the adaptor.
The garden hose adaptor thing can be found at any hardware store quite easily.
If a white plastic piece stays in the faucet when removing the aspirator, use a spoon ( like a screw driver ) to loosen it from the inside. Easy to remove, no damage done to the threads.
You need a SOLID, no water leaks, good connection to the faucet. ( Post has been slightly edited )