First off all, you want to get the wallet up and running...

Make sure you download the correct wallet for your system. Extract it to a place you will remember(Your desktop?)

Next you want to open the wallet for your system, and let it sync with the network. When it is ready, close the wallet by going to File -> Exit/Quit or use the shortcut Ctrl+Q.
 

You have succeeded in setting up your wallet.

Now lets mine.

Create your own execoin.conf (make a new text document and change the ".txt" to ".conf" with the following information:
(may need to show file extensions)

daemon=1
server=1
rpcallowip=127.0.0.1
rpcuser=user
rpcpassword=password
rpcport = 9988


Save it and depending on your platform, you move the file to one of the following folders:

Windows:

Go to your "Computer" folder and in the address bar, you type %appdata%. You will find a folder with the name "EXECoin". Move execoin.conf here.

OSX:

Go to finder, and in Go menu, you hold the alt/option button, you will see that there is a new location called "Library". Click it. You will find a folder called "Application-Support", open it and find the folder "exeCoin". Move execoin.conf here

 

Linux:

Go to your home folder, and select the option "Show hidden folders and files", you will see a .execoin folder. Move execoin.conf here.

 

Now you start your wallet again, and if you have done this correctly, you are ready to solo mine. Use Google to find a "Scrypt-Miner" for your platform, and point it to 127.0.0.1:9988