Firstly, it is possible the electrical utility may have to make upgrades to the transformer and/or the wiring from the transformer to the service drop, so consult with them before you start this project. You may also need permits and inspections depending upon where you live, so you need to research this.
Then, you'll have to buy and install a 200A distribution panel with a 200A main breaker.
You'll also have to have the meter pulled and the power disconnected at the transformer so you can replace the existing service entrance wiring from the service drop to the meter, and from the meter to the panel (the existing wiring will almost certainly not be large enough to safely carry 200 amps, so you'll probably need to buy enough 2-2-2 SE-U copper cable - I wouldn't touch either aluminum wire or copper coated aluminum wire -- to run from the service drop down to the meter and also from the meter to the new 200A panel). If it is feasible to install a new meter base and service entrance this might be easier as it would allow you to install the 200A panel, then run the 200A service entrance wiring through the new meter base and all the way up to the service drop (which would allow the utility to just switch the meter and service drop over, minimizing down time. You would then be able to dismantle and remove the old service drop, old meter base, and old service entrance wiring at your leisure).
If you do not want to transfer the circuits from the old 100A panel, you can install a breaker in the new 200A panel and use #4 wire (the size required to support 100A) to feed the existing 100A panel (depending upon what you are actually pulling in the existing 100A panel, it might not even require a 100A breaker to feed it). If you instead decide to tear out the old panel completely and just replace it, make sure to buy circuit breakers for the new panel which exactly match the amperage of the breakers in the old panel and place the new panel close enough so you can just transfer the circuits over to the new panel.
BTW, if you have this done and someone suggests installing and bonding another 100 amp panel (which is possible, my sister's house is set up like this with two separate 100A panels), don't do it. Having two 100A panels is not equivalent to a single 200A panel -- if you are going to all the expense and trouble to do this, do it right and don't compromise.