Help with washer

Hello all,
I have visited this link:
after discovering blothes of "grease" on my clothing (just colored ones). My washer is a third hand (or possibly even more hands) that I obtained from a honest family. The washer is an Inglis and it looks very old.
My question is: how do I fix the problem myself? All I can do is open up the top portion of the washer. I can see the washer housing but I don't want to proceed and not be able to put everything back together.
My other question is: why do the marks not appear on my white clothes?
PS - I don't use a dryer and I also do not use fabric softener, although the people before me might have.
Thanks for all of your help.

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