Upgrading or replacing your laptop's CPU/Processor is always a tricky thing since it undoubtedly voids warranty but can be cost efficient for doing it yourself especially when it is out of warranty.  When replacing your current CPU to a same model, you simply have to find the exact type of CPU you have.  When you want to upgrade your CPU, you must know what your laptop's motherboard is compatible with.

Knowing what you want and what you need:

1. Make sure you know exactly what specifications your motherboard requires.  The best way of finding this is to know the specifications of your current CPU.  Since many CPUs have different specifications, Intel and AMD, the two leading CPU makers, have many different types of processors with a combination of specifications and most are not compatible with each other.  For example, you have a Pentium 4 laptop, you cannot install a Pentium M Centrino CPU in it because first and foremost it will not fit into the CPU socket.
2. Best way to find out your current CPU's specifications is to download a stand-alone program called CPU-Z.  It does not require you to install it onto your computer but you can start it and it will show you the speed and specifications of your CPU.
3. Take a look at your current CPU's name, for example Intel Pentium M 750 1.86GHz.  You also want to look at its speed, L2 Cache and bus speed.  When replacing or upgrading your CPU, you don't want to install a processor that has slower specifications.
4. Always match your bus speed (FSB).  One example where you do not have to have match FSB speeds are with Intel Celeron and Pentium CPUs.  Celeron M CPUs run at 400MHz FSB and some latops can actually run a Pentium M 533MHz FSB in place of it.  There are two kinds of Pentium M CPUs, one with a 400MHz FSB and one with a 533MHz FSB.  You want to find out first if your laptop can take 533MHz before installing this CPU.
5. One important specification you want to look at is its "package," which is basically its socket type.  This is a physically number that represents the number of pins your CPU has.  You must stick with this number or else your new CPU will not fit.

Some recent CPU sockets for reference:

• Intel Dual Core: Socket M (Intel Core Duo, also called "Centrino Duo," Intel Core 2 Duo, and the new Celeron line like the 430)
• Intel Dual Core: Socket P (The latest Intel Core 2 Duo line-up called the Santa Rosa chipset, uses 800MHz FSB like the T7700)
• Intel Pentium M Centrino: Socket 479 pin.  Even though Intel advertises Pentium M processors as 478 pin, it is in fact 479 pins.
• Intel Celeron M: Socket 479 pin (Intel Pentium M and Celeron M use the same socket)
• Intel Pentium 4: Socket 478 pin
• AMD XP mobile: Socket A (462 pins)
• AMD 64 mobile: Socket 754 pin
• AMD Sempron mobile: Socket 754-pin
• Note: You generally do not want to cross over to a different "family" CPU to avoid compatibility issues.

Uninstalling and installing the CPU:

1. Before doing anything, unplug your AC adapter and remove your laptop's battery.  Never work in a carpeted area to avoid a static discharge which can destroy your computer.
2. Locate where your CPU is.  Newer model laptops are more easily accessible as they have a compartment under the laptop with a removable cover.  Some are located inside the laptop under the keyboard or are not accessible so getting to it may be more tricky.
3. A CPU will always have a heatsink metal assembly over it that also houses a fan to disperse heat.  Removal of the heatsink usually requires you to unscrew it and lift it off slowly from the CPU die.
4. CPUs usually have a type of thermal adhesive between the CPU and the heatsink to properly transfer heat over to the heatsink.  Some CPUs do not have thermal tape but have a type of foil instead.  Remove the old thermal tape with a cotton swab and use a cotton swab dipped with rubbing alcohol with atleast 90% alcohol to clean both the CPU die and the heatsink.  Clean the new CPU's die also.
5. You will need a thermal adhesive to install the new CPU.  Many computer stores carry thermal adhesive and it should look like a white paste.  Some enthusiasts use Artic Silver 5 thermal paste since it uses silver compound that transfers heat more efficiently and lowers temperatures.
6. Apply the thermal paste sparingly using only about a drop size on the CPU die and on the heatsink.  There are several methods on spreading the paste on the die and heatsink.  You can use a latex glove and use your finger to spread the paste, a credit card to spread the paste, or a plastic bag over your finger.  Just make sure the paste covers the whole CPU die and the area on teh heatsink where it touches the die.  Make sure you don't get any paste on other parts of the CPU other than the die.  Some CPUs like the Pentium 4 have a transfer plate that almost takes up the whole CPU, you can apply the paste to the whole metal transfer plate.
7. Carefully place the heatsink on top of the CPU and screw the heatsink into place.  Do not overtighten the heatsink but the screws should have retention springs to prevent overtightening.  Screw your laptop back together and start it up.

Testing the CPU:

1. Once you have booted onto your operating system, start up some applications and run some CPU extensive programs like Adobe Photoshop.  Some thermal paste need some time to become fully efficient.
2. A great CPU testing program out there is Prime 95.  It fully stresses the CPU so ensure stability if your CPU can handle it for an extended period of time.  I usually run the test for more than 12 hours and if it doesn't find any errors, I'm confident the CPU is stable and the thermal paste and heatsink are properly applied.  You can find Prime 95 by googling it, it is a stand-alone program that does not require you to install it.