There is no way with the current voting processes that anyone can verify that their vote was counted correctly in the final tabulation. The emphasis on "secret ballots" in construct of those processes prevents that.
As the stand up comic has joked, "Someone asked me who did I vote for? I said I don't know. Our voting system is so secret, even I don't know for sure who I voted for!"
It should be no laughing matter that with our current processes, you will Never be able to know for sure "who you voted for".
While technology has been applied to try to improve accuracy, that accuracy remains in doubt because the government and interested PACs are still focused on "secrecy" - instead of "privacy". But, only the private individual voter can truly verify the accuracy of their vote, and thus the integrity of voting.
Meanwhile, because of technology, your ballot is Not truly "secret". There are already ways the government and the election agencies could find out - if they really wanted to - how you marked your ballot: a) matching your finger prints - which are on any paper ballot you've submitted, b) same for any touch screen computer based ballot - your finger prints could be matched to your vote, c) matching epithelials on a ballot to your DNA, d) any sequencing process that correlates ballots with voters at a precinct. Remember, where you are registered to vote, and whether you've voted in the past are already matters of public record. The precinct size drastically limits the "search population" for anyone looking to see how you voted in a precinct. Thus it is not impossible for a determined "someone" in the government or election agency to figure out who you voted for.
Secrecy, or Privacy is the issue some people will howl about whenever someone says they want to know if their ballot was counted correctly in the final, official tabulation. But as anyone knows, "Secrecy" and "Privacy" are not the same. We can have Private Ballots in this country where you could verify who you voted for. So far our elected officials and government agencies show no sustained interest in constructing such a system.
And yet we implement systems that maintain Privacy in other important aspects of our lives in America. Consider your individual financial Privacy...
We go to great lengths many areas of American life to protect financial privacy. We've constructed amazingly accurate and hack-proof systems to ensure privacy. You must verify your annual income with the IRS to the very penny every year, and it is private between you and the IRS. No politician, PAC, ... nor your boss at work can look at your tax forms you've submitted to the IRS. Then, with one or more your chosen private financial institutions, you can verify your account balance and transaction amounts to the very penny every day for every transaction you conduct within your private account. The integrity and privacy of the supporting systems is far greater than our voting systems. You, not your senator or boss, know your private account number, your user name, and your private PIN or password, which unless you've posted all this on Facebook or Twitter, it's usable by only you. Millions of private transactions are conducted daily, accurate to the penny and verifiable. While hackers allegedly try daily, and once in a while have succeeded in obtaining credit card numbers - usually from retailers, it's not the same as your brokerage, cash savings or checking accounts which have tighter security. And unlike with voting, you will know if a money account of yours has been compromised, used without your consent, and you will have it restored its correct balance. Banks and brokerages that fail to do this for you can be brought up on criminal charges... If you are not happy with the level of privacy and security at one financial institution, you can choose to close your account and go elsewhere.
A system that tallies votes like we count money that is accurate and private for each vote and verifiable by each voter is obviously possible.
Other posts here have noted how the use of private "accounts" and private "keys" will pave the way for this.
"We" just haven't been willing to invest in such a system.
So the way things are now in America is this: You, the individual are required by law to annually submit a completely accurate to the penny account of your income to the IRS, under various penalties for falsifying data including fines and jail time.
But when it comes to the very reasonable and simple request for the government to show you how your vote was counted in the final tabulation of any election, the bottom line is the government must only tell you, "Trust me"...