This page gives you instructions on how to update your firmware to 4.2 or 4.3.This lets you get the features of those updates without the chance of bricking that the newer update might cause (as long as you haven't previously done nasty stuff to your Wii).Either of these firmwares is safe, so feel free to choose either one.
Follow the PART 1 steps before performing one of the following methods.
Each of these methods will install 4.2 or 4.3 in a safe manner, but they have different pros and cons.
It is most recommended that you use the Nintendo's Official Update methods.
The third 4.2 method is the most complete without having to reinstall other things, but may require several tries (and a lot of time) to work.
The 4.3 method is the easiest method and most recommended.
PART 3 is optional and allows you to block future disc and network updates that are not yet released at the time of writing of this tutorial.
For more information about upgrading, see the Upgrade FAQ.
Note that a power outage might brick your Wii, so do not perform these steps in a storm or other situation where power outages are likely to occur. There are then several methods you can use to upgrade to firmware version 4.2 or 4.3 (in PART 2).
The first is probably the best 4.2 method, but may require you to complete the new d2x steps if you haven't done them before.
The second 4.2 method is very quick, but is not a complete upgrade to 4.2 and is not recommended unless you are on 4.0 or 4.1.
It will not upgrade the IOSes for your games and they may still ask to upgrade, but those updates should be safe as long as the games are from your region.