The process of giving notice depends upon the nature of your claim.

If you are pursuing a claim under the federal Tort Claims Act, you must submit your written claim to the agency official who has been designated by the agency to receive FTCA claims. That would normally be done by using GSA form SF95. The claim must normally be submitted within two years of the date upon which the cause of action accrued. Filing a late claim can cause your claim to be denied, no matter what its merit.

Once you exhaust your administrative claim, including any administrative appeals within the agency, if you did not obtain adequate relief you may file a lawsuit in federal district court. You will normally have six months from the date the agency issued its final denial of your claim to commence a lawsuit. If you do not file your claim on time, it will be time-barred.

The process for contract claims is different, but as you speak of constitutional rights that process would appear to be irrelevant to your question.

The statute of limitations on your action will vary depending upon the nature of the claim you file (its statutory basis). Be careful not to miss the deadline set by the statute of limitations when pursuing your claim.