in your office you will have 30 workstations computers all running
Windows Xp Professional and in another office across the country you
will have 10 workstation computers all runiing windows Xp professional
every computer must connect to every computer in either office and
well as the internet? How should this network be design? What type
network should the computers at each office be connected to? At each
office should a server be added? What network topolology and protocol
should be used?

Connect to control the other computer, or to only access files?
To control it, you need RDC (Remote Desktop Connection) its built into XP Pro.
To get files off of it, you need to set up either a FTP, or VPN to a server.

Sounds like a homework question, or an MCSE preperation question.

If you want the overkill Micosoft answer then;

You had 2 servers at each location, an active directory server,
running DNS as the name service, not WINS, and an ISA server. You then
get cable, DSL or any other permanent internet connection at each
office. Configure each office to use reserved internet address, eg
office 1 uses 10.0.1.* and office 2 usese 10.0.2.*. Configure
workstations to route through the ISA server, picking up their TCP/IP
settings via DHCP from the AD.

Now check internet access works.

Then configure a permanent VPN between the two ISA boxes, and
configure the AD servers to exchange their information between each
other, so each office can get routing information by machine name, and
lo, you have a secure connection between offices.

http://www.isaserver.org/tutorials/hubandspokevpn.html has a guide to
using ISA for remote office setup, as does
http://www.microsoft.com/technet/prodtechnol/sbs/2000/maintain/remotofc.mspx

http://www.microsoft.com/windows2000/techinfo/planning/activedirectory/branchoffice/default.asp
has a planning guide to setting up remote office networks using AD.

You are using - 30 XP Workstations for Intranet1 and 10 for Intranet2. 
No need for the server as such.

If you are asking the basics about the topology and protocols. Three
commonly used protocols are Ethernet, Local Talk and token ring.
Topology used can be Star, Bus, Ring, Tree. I recommend Tree which
combines features of linear bus and star topologies. It consists of
groups of star networked workstations connected to a bus backbone
cable.

WS1     WS2   WS3       WSn 
 |      |      |  ....   |  
 ------------------------  <- bus

          WS1  
           |
   WS2 - Switch - WS3
           | (star)
          WS4 
Twisted Pair and Fiber for Bus, Coaxial cables for Star are used. 

For this particular case Star topology can be used. IP Router(NAT),
Switches or a couple of switches can be used for accomodating 30
systems.

Each network should have a router. You can connect both the networks
using dedicated or dial up links. The two office routers are connected
to the Internet using local dedicated or dial up links to a local ISP.
A router to router VPN connection is then initiated by either router.
Now they can forward traffic to each other.
                     ____________________
               ISP1  |     vpn conn       |  ISP2
   [Intranet1] ~~~~~~~====================~~~~~~~ [Intranet2]
                     |   Internet Cloud   |
                     |                    |
                      _____________________