Its quite easy on computer a you don't need to do anything just make sure both system are on same network if its not internet access(for this you need static ip). Okay now on computer b go to start menu find configuration under oracle folder click Net Configuration Assistant under that folder when window pop up click Local net configuration option it must be third option.
Now click add and click next in next screen it will ask service name here you need to add oracle global database name of computer A(Normally I use oracle86 for my installation) now click next next screen choose protocol normally its tcp click next in host name enter computer A's name you can found that in my computer properties. Click next don't change port untill you have changed that in Computer A click next and choose test connection now here you can check your connection working or not if the error is username and password not correct then click login credential button and fill correct username and password. If its saying unable to reach computer ot target not found than you must add exception in firewall for 1521 port or just disable firewall on computer A.