I bought a couple of large syringes and plastic tubes for this very purpose, folk sell them on eBay for next to nothing and they are handy bits of kit to have. Here's how I do it on my RSV Mille for both the brakes and the clutch :-
1. Clean around reservoir cap area
2. Remove brake reservoir cap
3. Using one of the syringes, suck out the old fluid in the reservoir and clean
4. Fill resevoir with fresh fluid
5. Fill other syringe with fresh fluid and fit using plastic tube to bleed nipple on caliper
6. Crack bleed nipple open and slowly begin filling from syringe, watching the level in the reservoir
7. As reservoir fills up, remove the excess ( When you stop pressing the syringe to remove the excess before continuing close the bleed nipple first and then crack it open again to continue filling
8. Rinse and repeat until fresh, clean fluid starts to appear in the reservoirWhen it does, stop, tighten bleed nipple and then refit reservoir cap
9. Or before refitting reservoir cap, transfer syringe over to bleed nipple on other caliper and repeat until old fluid in that side of the system is expelled and again, fresh fluid starts filling the reservoir up
10. Once you are confident that you have completely fresh fluid now in the system, stop, tighten bleed nipple and refit reservoir cap. Job done.
Be careful when you fill the syringe to make sure you do not create air bubble ie suck it in slowly. If you have to refil the filling syringe make sure that you do not introduce air into the system - make sure the fluid is to the top of the pipe when you push it on to the nipple. You may need to turn the bars to make sure there is no high spot in the system.
There is no order to which leg you do first.
