Are you in the situation that the Ethereum hardfork leaves you with ETH and ETC entitlements on both blockchains? If yes then this post might help you.
First of all, pause for a moment and do not engage in any ETH or ETC transactions. Take the time to educate yourself in detail about the current situation and mechanics, before you move any of your funds. Else you can find yourself in the situation of loosing some or all of your ETH and ETC by clumsy manipulations, parallel spending and/or replay attacks.
There is very little room for trial and error. I personally lost parts of my holdings until I fortunately figured out how to secure the larger part.
Throughout the recovery process, explore the current status of your holdings on your addresses on both blockchains. For ETH, use etherchain.org (access search in the upper right link) and for the ETC chain gastracker.io, which works by typing"gastracker.io/addr/" in your browser and then adding your ETC address (which is the same like your ETH address) right after that (Enter).
Depending on where your ETH and ETC sit, take different measures:
Mist Wallet & Browser
As a great start, read Vitalik's blog post on the Ethereum.org Blog:
At the bottom of his post, he refers to a convenient step-by-step guide which could work for you to split your ETH and ETC. However the splitting contract might not work. Typically, this seems to be the case if there were transactions in your addresses after the fork. It also might be that the splitting contract only works once for a given address as well. So if you call the function to try it out with small amounts, the remainder of the ETC holdings might be stuck. Moreover, please see further below: the splitting contract may exhibit unexpected behaviour.
In any case, if you have several ETH/ETC addresses concerned, start with the ones with small holdings until you gain comfort.
In the case you can't make any progress, there is no way around setting up the Mist Wallet for ETC to access ETC. Best, set it up on a separate computer. Use the post fork version in any case. If you do not have a separate computer, you can also use your current Mist Wallet and change it from ETH to ETC. For both options, the guide for setting up an ETC Wallet can be found here. The wallet worked better for me than the browser option. The chain download for ETC can be as quick as 30 minutes. Do not move any funds yet!!!
Make sure you setup new addresses before you move any funds and move them to the new addresses only! This Reddit post helped me a great deal to collect my ETC while not loosing my ETH. When you start using your ETC Mist wallet, you might be shocked that you see funds disappearing suddenly. In my instance fiddling with the ETC Mist version unlocked the stuck operation in the splitting contract and sent the funds to the address which I previously defined in the splitting contract which was with Poloniex! If you have other tokens than ETH attached to your addresses, make sure to secure these as well to new addresses.
Poloniex & Kraken
If you had wallets at Poloniex & Kraken, you are lucky: your ETC should have been made available to you as a service already.
Coinbase
You were excited that Coinbase added ETH support and sent them some? Bad luck, if in parallel on the ETC blockchain the same transaction ran for your ETC as well. Coinbase added ETH after the hard fork, is not supporting ETC, and might reply by referring you to this link when you ask them to refund your ETC. They might add their standard-sentence "I hope that helps clarify things! Let us know if you have any other questions, and thanks for using Coinbase.".
MyEtherWallet
MyEtherWallet is also not supporting ETC, but you can access your inherited ETC holdings. Here you can find out how.
Other Wallet / Provider
There are dozens of ETH wallet providers which might or should have access to your ETC if you carried ETH with them through the hardfork. Few have implemented solutions to hand your ETC holdings over yet. Don't hesitate to contact them and insist on receiving what is yours!
Closing note: Personally, I did not expect ETC to persist after the hard fork and prefer that it doesn't. I'd like to find the whole ecosystem united again, preferably with the evolving and more human Ethereum protocol version. While there are still too many ETC enthusiasts which find value in the old chain, I happily went through the hassle to claim my ETC and made it available (for a modest purchase price of course). Good luck!