You can solo mine bitcoins with any of the following:

CPU

Graphics card

FPGA

ASIC

CPU mining is not very efficient and the chances of finding a block using your CPU is very remote.

To mine bitcoins you also need some software to mine with. The most popular ones are cgminer and bfgminer.

Create a Bitcoin Wallet

If you do not have a Bitcoin wallet then you will need to create one. There are many different types of wallets you can choose, however, to keep this guide as simple as possible I will direct you to https://blockchain.info/wallet. Start a new wallet and follow the on-screen instructions. When you have finished it will display your Bitcoin Wallet address for receiving bitcoins. Take a copy of this as you will need it later.

Bitcoin wallet at Blockchain

Software Installation

cgminer – mining software

Bitcoin ASIC Hardware

Follow this section if you have purchased bitcoin ASIC hardware.

Download and install cgminer from cgminer homepage
Create a file named start.bat in the same directory you installed cgminerEdit the file and put in the following:

cgminer -o stratum+tcp://stratum.bitsolo.net:3334 -u 1KbfPjjpwu5undFfGULwYpVyvo8gpdpCGH -p x

Change 1KbfPjjpwu5undFfGULwYpVyvo8gpdpCGH  to be your Bitcoin address.This is the address payments will be sent.

Run start.bat by double clicking on it.

You should now have a window with cgminer running and mining for you.

Graphics Card

Following this section if you are planning to mine with your graphics card.

Download and install BFGMiner version 3.6.0 from BFGMiner Download. Additional instructions can be found from BFGMiner Homepage.

Create a file named start.bat in the same directory you installed bfgminer. Edit the file and put in the following:

bfgminer -o stratum+tcp://stratum.bitsolo.net:3334 -u 1KbfPjjpwu5undFfGULwYpVyvo8gpdpCGH -p x

Change 1KbfPjjpwu5undFfGULwYpVyvo8gpdpCGH  to be your Bitcoin address.This is the address payments will be sent.

Run start.bat by double clicking on it.

You should now have a window with bfgminer running and mining for you.

Watch and Wait

You need to keep your miner running at all times to mine. To find out if you have found a block look at the Best Share column on cgminer or BS on bfgminer. This will tell you your Best Share found so far. If this is higher than the network difficulty then you have found a block.

Additionally, when you have found a block it will show up in My Account tab and then be sent to your Bitcoin address .