How to bleed the clutch?

I drive a Spectra5 and recently had to replace the clutch master cylinder due to seal leaking brake fluid at the clutch pedal. The brake and clutch system are fed from one reservoir that is attached to the brake master cylinder. After replacing the faulty part I bled the system thru the clutch slave cylinder. However now it feels like the clutch is engaging differently. When either taking off in first gear or switching gears while driving it seems that the clutch is engaging when the clutch pedal is almost all the way to the top of the pedal stroke instead of a lot lower like before. Could this be an indicator that there is still air in the line? If so, what is the correct process to bleed the clutch system and do I also need to bleed brakes at each caliper?