It depends on which state: (where I live, no anonymity when claiming, where I have played you can claim anonymous).
Don't say a word to anyone and remain calm, giddiness would probably make bad things happen. This is the first rule.....the rest is a Rough Draft
1.) Make copies of the ticket. Put original unsigned ticket in a fire proof safe.
2.) Rent a cheap apt/efficiency and change my legal address to the apt/efficiency. Disconnect my landline in my home. Put a for sale sign up in front of my house. I would get a P.O. Box and a safe deposit box for anything else. Possibly look into a leave of absence.
3.) Meet with an atty to discuss safeguards to protect my family and the winnings while looking into paying off various debt: mortgage, cars etc. It might be advisable for me to keep my mortgage (for the interest deduction in the year that I claim for tax puposes). I would look into setting up a a family limited partnership or a couple of trusts. (one to put my home and the bulk of the winnings, another to help pay for my kids' needs: schooling, clothing, etc. nothing extravagant.) Look into setting up some type of charitable trust to benefit a couple of oranizations near and dear to my heart. Also I would need to determine whether the publicity would hurt me as far as work goes (would it be wise to resign, not because I want to, because I wouldn't want someone to sue me in some frivolous lawsuit.) If I had to resign I would have to set up some type of "living account" that would provide income to pay for food, healthcare etc. Discuss various insurance needs that I may need for estate planning purposes (policies that would help pay any expenses upon my death so my children aren't left with the burden). I would also ask if my immediate family (parents and siblings) could claim some of the winnings and draft up a tentative agreement stating their share of the claim. Being that I would have to pay gift tax on anything I give them above 13000 ( if I claim it all for myself), it may be better for them to claim a share, pay the taxes and have more right up front. This may take several meetings that would later involve a tax advisor. Pre-print the claim forms and tax forms. Since I have experience with investments, I would look to set up a new/separate cash management account to deposit the initial "check"
4.) Sign ticket, as advised, Go with attorney (and family) to claim the winnings with the original ticket and a couple of copies and the. claim forms. In my state, request "no press conference" my name, will already be public record. If I win in the other state, just claim anonymously and lay low.
5.) Wait for my share to be deposited in the CMA.
6.) Disperse funds to the various trusts from the CMA. Sign over home to trust, take down for sale sign, change back to original address. I would try to have enough money set aside to live off the interest/dividends if no anonymity( I would have to quit my job), the money that I set aside in the "living expense account." Using what I live off of, I would then diversify into equity based mutual funds for long term growth, much the same way I do now. Ladder some into CDs. If I claim anonymously(in the other state), I would keep my job, and I would not buy anything extravagant and noticeable until after a couple of years. I would probably be more agressively invested than CDs....
7.) If winning the jackpot means "set for life", I would quit playing because, the chances of it happening again are slim to none,and it would give someone else a shot at it.