Copying/pasting in what I posted elsewhere in 2014:
Declare both royalty and bonus income on Schedule E of your federal income tax return.
For royalty income, be sure to drop in the gross royalty, then show the deduction of severance taxes and other deductions, if any, which were subtracted on your check stub. That way, you can take 15% depletion allowance on the gross, rather than the net. In other words, you want your 15% depletion allowance calculated on the larger number. Bonus income, on the other hand, is entered as rental income, and you don't get to subtract the 15% depletion allowance.
Be sure to report the income shown on your Form 1099's each year. It means that you calculate the royalty and bonus income for the year depending on the date of the check, not the date your received it. If you try to balance to your bank deposits each year, for example, you will need to adjust for checks dated in December and not received until January, and these timing differences can occur at both the beginning and the end of the tax year. If your royalty and bonus income don't tie to the numbers on Forms 1099, you are more likely to get an inquiry or an audit from the IRS. Examine the Forms 1099 as they arrive, and if any are wrong, especially if income is higher than actual, call the company right away to ask for a corrective Form 1099.
You can subtract out-of-pocket expenses attributable to the Schedule E income. I subtract NARO dues, DrillingInfo.com fee, FedEx overnight mailking, copying at FedEx/Kinko, maps bought from Midland Map Company. Also I keep a detailed log of toll calls and deduct that expense. Once I bought an expensive huge locking ring binder which I would be using forever for my oil and gas reference notebook, so I deducted it as office supplies. I don't try anything fancy such as home office deduction because I use my home office for other things. The Schedule E layout wants you to drop each out-of-pocket item in the column for a specific property. I have multiple tracts and if the expense is easy to attribute to a specific tract I drop it in that column; otherwise, I drop the expenses in against the tract producing the largest income. I generally enclose an exhibit showing exact details of the out-of-pocket expenses, indicating whether I have a receipt for each (i.e. I don't enclose copies of the receipts but rather I indicate on my exhibit that I do have the receipt in my file), so as to reduce likelihood of inquiry or audit. I file federal and two states, by the way--my state of residence, as well as the state where the mineral interests are located. "Ugh" is right.
You probably already realize the IRS website easily allows you to open up Schedule E and take a look at it, or print it to paper.
There is continual pressure from some politicians in Congress (and the current occupant of the WH) to eliminate the 15% depletion allowance. You can join National Association of Royalty Members, and make additional contributions to their lobbying arm, if you want to do help.