in the middle of a string, use two single quotes next to each other to include a single quote in a string. For example:

declare X varchar2(1000);

begin

X := 'This is kmesser''s string'; - between the r and s are two single quotes
insert into kmessertable values(X);
X := ''''; -- that is four single quotes in a row, which will result in one, single quote being stored in X as a varchar2 value;
insert into kmesstable values(X);

end;