I have a 95 civic coupe with a JDM D15B vtec engine. I'm not sure what kinda tranny or fluid is in there. I just bought the car a few weeks ago. It was shifting fine when I got it but it starting acting up once it got cold.

So here's the problem:
When I start the car, there's not much pressure when i depress the clutch. Sometimes it gets stuck and won't even spring back up. Obviously I can't get into any gears. After a long warm up and pumping the clutch pedal a bunch, it works fine. If I turn the car off, I can put it in gear and then start the car and go.

What's going on?

 

Clutch hydros.

Look under dash at the clutch master cylinder and see if fluid is leaking.

Pry the dust boot back a tad on the clutch slave cylinder and see if fluid is leaking.

I would replace both...you have hardly any disengagement.

 

How much do those parts cost and if I had a mechanic do it for me, how much should I expect to pay?

 

Japanese specialty shop would charge from 2-4 hours labor @ 60-100/hour. So, from 120-400 labor. And parts depend on what they use. Nissin(OEM Honda) units can be cheap, when purchased under the brand "Adler". Parts should be under 100 for both