how is conducting research online different from conducting research
in a traditional library

Online research is very much based on keywords. After one or more
search engines are selected, the big part of the research process is
finding the good combination of keywords to narrow the results of the
search. Then it is very much experience that allow you to recognize
quickly what website will contain the information you are looking for.

When conduction a search in a traditional library, you will use
titles, authors, dates, topics. The only keywords you will use here
are for the title.

example:
you are looking for how to make bread. An online research will consist
of choosing keywords like "bread", "yeast, "make bread", "bread
machine" ... and according to your first results, you may even find
other relevant keyword to guide you to more specifics. when you will
have learnt that gluten is an important ingredient, you may look for
"gluten" in a new search. You will likely get small articles,
pictures, receipes, and you will have to combine that to get what u re
really looking for.

in a library, you will have to search differently. you will want to
look for the cooking books section for example. You are likely to find
a few 300 pages books with 'how to make bread' explanations,
receipes...  But you are also likely to miss some information or
anecdotes hidden in an history book or some links to the latest bread
machine vendors with reviews and all that.

so my conclusion would be that an online research will bring you a lot
of small information, relevant, but also irrelevant and you will have
to work harder to sort the information, but it will be easier to find
some precise piece of information.
A library research will bring you results that may not fit your
question as well but a book will be a more detailed source of info
than a web article.
The very latest news will be hard to find in the library

The good way to go is to combine both, like trying to find the good
books from an online research... ?

As a librarian who uses both research methods daily I can second the
above comment.  Traditional library research is often much more
cumbersome, time consuming, outdated but it's results can be more
accurate, detailed and satisfying.  Online searches can be quicker,
more precise, more up to date but can result in unreliable sources and
a lot of information to filter through.

For overviews of subjects or subjects which are very large and
detailed traditional research is usually the way to go.  Books are
good for culling together information from many sources and presenting
it in an organized way.  Online sources are catching up with
encyclopedia type pages such as Wikipedia but it suffers from the lack
of reliability.  Also there are many areas that are reletively
untouched by online sources.  Research collections consisting of
primary sources, personal collections, genealogical information,
information in thousands of older books, and many other things are not
yet available online.  There are things that just cannot be found
online in any way, shape, or form.

Online research makes it easy to find precise answers.  It is often
hard to find information in books because either there were no books
written on the subject, many books are not indexed or the information
is outdated.  Online research is improving daily as many traditional
sources are being digitized.  And because the Internet is not a static
source it is extremely useful for the most up to date information. 
Books are often obsolete by the time they are publsihed.

This is just my 2 cents.  I'll reserve a full answer for one of the researchers.