It's not recommended to change just the lifters. The cam and lifters should be replaced together. To get at the lifters, you can remove the rocker covers and intake manifold, loosen the rockers enough to get the pushrods out, then pull out the lifters.
There is no adjustment for hydraulic valve lifters. Lifters can be noisy on some of these models. After ascertaining there is no mechanical damage/broken parts, change engine oil and add 1/2 bottle of STP Oil Treatment (or more if necessary) until lifters are quieter.
You find a book to the car or go to autozone.com and print the directions....then follow them.
try an engine flush at the next oil change, but it will most probably require replacement hydraulic lifters (tappets)
As you give very little information as to make, model, engine size or year, and exactly when it is ticking, this is just an educated guess. Normally this is valve noise caused by valve clearance issues. If it has solid lifters then they need adjusting. If it has hydraulic lifters, they may be clogged and sticking. If it has hydraulic lifters try adding a can of Seafoam engine tune to a fresh oil filter change. It can be purchased at many auto parts stores. Drive the car for 500 miles and change the oil and filter again. You may have to do this more than once to remove the deposits in the lifters. If this does not work, then the valve stems or lifters are worn, and need adjustment or possible replacement.
have the tappet settings checked.if automatic lfters,check engine oil for correct level correction, not automatic lifters,hydraulic lifters
Just the lifters and gaskets. It would me smart to replace the timing chain and gears too.
The oil change usually helps quiet the lifter noise. You could replace all 16 hydraulic lifters if it really bothers you. Most Miata owners just live with it. Try 10W/30 oil.
It is normally caused by sticking hydraulic lifters or lifters that need adjustment. Try pouring one can of Seafoam in the crankcase. If it helps then change the oil at your normal interval and then add another can. You can buy it at any auto parts store and Walmart.
Which part do you want to replace? The slave cylider or the master cylinder? The hydraulic line and master cylinder.
A ticking sound at startup can be a couple of things. It can be a worn drive belt, especially if it does not go away fairly quickly. It also can be a valve lifter noise. Check the drive belt and replace if necessary. Change the oil and try using a different brand oil filter. Purolator, AC/Delco, Wix, Motorcraft, are all good. I would use an OEM type filter to start with. If the car has solid lifters they may need adjusting. If it has hydraulic lifters and changing oil/filter does not help, purchase a can of Seafoam Motor Treatment. Often lifter noise in hydraulic lifters is often due to dirty and gummed up oil passages, varnished lifters and buildup of gum, varnish and carbon. Seafoam is an excellent product used by many auto technicians that will help clean the lifters. It can be purchased at most auto & marine parts stores. Follow the directions on the can to the letter. It is also an excellent Fuel Injector cleaner.
If we are talking about valve lifters, remove cylinder head and pushrods and lifters will be excessable.