Most individual real estate investors operate on a cash basis and fill out their annual rental income on an IRS Form 1040 Schedule E. On the income portion of this form there are three common errors that the IRS spells out in their instructions for residential rental property.
Rent is earned when you receive it. If you receive any sort of advance rent you report it in the year you receive it. Common examples are a deposit that is really the last month's rent. We might rent out a house with "first, last, and damage deposit". The damage deposit in this case is held for potential damages and may or may not be returned. The "last" portion is the last month's rent paid in advance and is income in the year we receive it, not for the month it's paying for (unless that's in the same year you received it as would be possible in a six month lease, for instance).
Expenses paid by the tenant are income for you the owner. If a tenant pays for a repair and this is deducted off the rent then you have two entries, not one. You show income for the amount spent and then a corresponding expense for the item repaired. For example, the A/C unit needs repair and you authorize the tenant to pay the $200 repair and deduct it from what would normally be $1000 in rent. Accounting wise, that month you still receive $1000 (the $800 from the tenant and the $200 spent by the tenant even though it didn't go to you). You also have a $200 expense for the repair. The net amount of the transaction is that you only received $800 (because the A/C broke) but you've now accounted for it properly.
Security deposits kept are income. Similar to both of the above, you need to account properly for deposits kept. If you have a $500 cleaning deposit and on move-out you discover that you're going to need to keep and spend $200 of it to get the unit ready for the next tenant then you now have $200 in income and a $200 expense for the cleaning. Since the deposit was intended for this type of thing you did not report it as income in the year you received it (assuming it was last year) but must now report $200 of it (in our example) as income. You'll also have a corresponding $200 expense (for the cleaning). The end result is $0 to you but it will be accounted for properly.
A couple of more examples of the above may be helpful. Let's say you agree to pay for water for your rental but every month the bill goes to the tenant and they pay it, deducting the amount from their monthly rent. If the full rent is $650 and the water bill is $20 then you still show $650 in income when the rent is paid each month even though the check you receive is only for $630 ($650 - $20 = $630). You'll also show an expense for the $20 water bill even though your tenant paid it. $650 in income. $20 in expense. The net amount is $630 which is what you received on your renter's check. It's shown in two parts like that even though you received the net as one check.
Let's say you rent a house out for $1000 per month with a $500 deposit used to pay for any damage upon the tenant leaving. Since theoretically it will be returned you do not show the $500 as income when you receive it. If, however, when the tenant moves out (for example next year) you end up spending $300 for cleaning and repairs and giving back the other $200 then that $300 spent would now become income in the year you determined to keep it (when the tenant moved out). Your actual expenses for the cleaning and repairing are then deducted from your total income as an expense. Unless you kept more or less than the actual cost it should end up a wash, accounting-wise.
One last example straight from the IRS publication on rental property is where perhaps your tenant is a painter and you work out a deal where he paints your house in exchange for two months rent. On your books you would show "normal" income for whatever the rent would have been and a corresponding expense for the same amount under "painting". You will want to watch out for this, though, as you may be trading current income for something you have to write off over time, like a new roof or a kitchen remodel, etc. You can read more about that at repairs vs improvements.