There are several different homebrew applications that will check your system IOS's but sysCheck is by far the easiest to use and it gives an accurate and detailed report. Here is how you would go about creating a system IOS report and posting it in the forum.
Creating a system IOS report
A1. Download sysCheck 1.6.1 here.
A2. Extract the files and copy them to the sysCheck161 folder in the apps directory of your SD card. It should look like this SD:/Apps/sysCheck161/all the files
A3. Put your SD card in your Wii, enter the Homebrew Channel, and load sysCheck.
A4. The application is fully automated. It will scan every IOS on your system and it will exit back to the Homebrew Channel when it is done. In that process sysCheck will create a report in the root directory of your SD card. SD:/sysCheck.csv
Viewing the information and posting it in the forum
B1. Put the SD card into your computer. You can view csv file by opening with Microsoft Excel or the text editer of your choice (Microsoft Word, Wordpad, Notepad etc). If your are going to post your results in the forum I recommend opening it with Excel, Word, or Notepad++ because it lays out the information better and makes it easier to read.
B2. Just cut and paste the information into your post so that whoever is helping you can see it.
B3. You may backup or delete the sysCheck.csv file or leave it on your SD card if you wish. It will get overwritten next time you use sysCheck.
How do I check my IOS's if my Wii if HBC is corrupt
C1. Backup the contents of your SD card to your computer. Erase it's content and format it to FAT32 if it is not already.
C2. Download CB2_BB_SysCheck_1.6.1.zip and extract all the files and folders to the root of your SD card.
C3. Put the card in the wii and click on your SD card button. Load boot.elf.
D1. Copy the sysCheck boot.dol to the root of your sd card. Put it in your wii and load up priiloader.
D2. Scroll down and select "Load/Install File". Highlight Boot.dol and "press 1" on your wiimote.
If your want to learn more about system IOS's and cIOS's, what they are and what they do, take a look at this thread.
If you are getting a blackscreen loading a game and want to check if you have the right IOS to run the game look at this thread.