You do need to do it right. The BLM will take your money and register the claim. The same with the county. If both places take your money and give you stamped paperwork, does not mean you have an official claim. It's your responsibility not theirs to be sure you have staked a valid claim. There is no checks and balances for this by the govt agencies. They only take your money. The only check and balance is once you set foot on a claim that is not yours how the land owner or claim owner decides to treat you. People have bought gold claims off E-Bay in AK, flown up there to work there claim and had guns pulled on them telling them to get off by the rightful claim owner.
I recommend this site:
http://www.mylandmatters.org/ You can only stake a claim with the BLM on Federal land; however, if you send them a form with the correct fees, they will send you paperwork for mineral rights, but if you have paperwork from the BLM saying you have mineral rights, if its not on federal land, it is not valid. They will even send paperwork on claims on federal land withdrawn from mining (National Parks, Wilderness Areas, an mineral withdrawal areas). Several years ago, looked at staking a claim in Alaska and did not get far. I remember reading that state land can be easier then federal land, but I'm in AZ and never went through with it.
In AZ, I do three things. I check county records to see if they are filed. Yavapai county allows searches on line for free. Maricopa County charges $1 per record retrieved by PDF. If I see there is no claim filed in the county, I will go to LR2000 on the BLM site to see if anything has been filed. Once I get an area I know is not claimed, I check land status from the state site azland.gov. Reason I check land status is the BLM land is often patchworked with other than federal land. In AZ, approximately one section per township / range is dedicated to state trust land. Also, some places have every other section private property and BLM land. The county need only be filed with once, but the BLM needs to be renewed every year by Sep 1st. So if the Sep 1st deadline is missed within the next few months the BLM will show the claim closed and it can be refiled. Setting foot on ground is important. If someone has filed a claim, two weeks can pass before the county system shows it in the online database, so you could get there and see a monument.
Big thing about checking land status is once you're familiar with the process you will find claims that are filed with the BLM where they shouldn't be like private property, state trust land, and over patented claims.
In AZ prospecting state lands is not off limits, just prohibitively expensive (thousands of dollars for a claim to look for minerals and not mine them). Alaska state land is supposed to be easier.
Took me eight months to learn how to stake a claim in AZ. In AK the concepts would be the same:
1) Check land status to make sure its federal mineable land
2) Check county records for filings. Hopefully on line.
3) Check BLM for active claims
4) GO TO THE AREA, prospect, and then stake if worth it.