You are really asking for trouble if you "just throw them all together."
This sometimes works, but more often it can be a recipe for disaster -- and
can result in a situation where it will be extremely difficult to undo the
damage.  It is important to do this very slowly and carefully.  It is much
better to err on the side of caution and take extra time than to do the
reverse.  I adopted Duffy a year ago and wanted to bring him into a
household with my previously-very-jealous cat, Holly.  The two cats now get
along beautifully.  I have a fairly lengthy explanation that I wrote that
explains the process I used.  Please send email if you would like for me to
email it to you.  The email address attached to this is valid, except that
you need to "take out the litter" first.  You can also see pictures of what
I did if you look at the two albums (especially the first one) below my
signature.

There are also a number of sites on the Internet the provide information on
introducing cats.  Here are some of them:

http://www.catcaresociety.org/intro.htm
http://www.ddfl.org/behavior/catintro.htm
http://www.cuhumane.org/topics/catcat.html
http://www.methuen-mspca.org/petcare/htm/catintro.htm
http://operationnoblefoster.org/catsanddog.htm
http://www.catsinternational.org/  (library of articles)
MaryL
(take out the litter to reply)

Photos of Duffy and Holly:      >'o'<
http://tinyurl.com/8y54 (Introducing Duffy to Holly)
http://tinyurl.com/8y56 (Duffy and Holly "settle in")

I would recommend several different things that will help.

Before the introduction, taking bedding used by the cats and exchange
them. This way, your cat is introduced to their smell, and they are
introduced to yours.

Another thing to do for the actual introduction is to put a tiny
amoung of perfume above their noses (same for everybody), that gives
them all a similar scent and makes them smell less different.

Another thing is to bring the new cats in and keep them in a room for
awhile and let them get used to the smells of each other. Lock the
current cat in a room and let the new cats explore the rest of the
house. Take turns with who is out. Then they get used to the new
smells without actual encounters. If you have a child gate and a way
to do it, leave them separated by the gate, so they can sniff and paw
at each other, but easily get away.

And for awhile, give them small sessions together with supervision to
make sure things go well. Give lots of treats and make it a great
experience for everybody. Make sure you give your current kitty and
dog lots of attention so they don't feel mistreated.

Meghan & the Zoo Crew  
Equine and Pet Photography
http://www.zoocrewphoto.com

Well, firstly I'd amend that statement to "they'll work it out in a
MONTH or two". Probably a more realistic time frame.

The best way is to achieve some physical seperation for a few days -
exchange scents and smells, follow that with limited supervised
interactions for a few days and THEN throw them all together and give
them another month plus to work it all out.

There are many opinons on the best way to introduce new cats.  I've had the
best luck with putting the new cats in a room with a common door to the
existing cat and letting them get "smell acquainted" before they see
eachother.  Let them sleep on some towels or beds and switch them the next
day so they can smell eachother.  Do this for a couple of days before trying
to introduce them visually.  Also, gender matters in this case -- females,
even spayed ones, are much more territorial than males.  If one of the two
new cats is a male, introduce him first, after a day or two of "smell
socializing."  It also may help if you can keep the dog away while the cats
are meeting -- the idea is to limit the new information the new cats have to
deal with at first.  Let them get to know your cat for a day or two before
introducing the dog.  Your sister is right that if you throw them all in
together they will eventually work it out, but they may work it out in such
a way that they establish adversarial relationships right out of the box,
and that can take quite a while to resolve.  Good luck! -- L.