With an EV that you charge at home, you generally don't get a separate EV charging bill (although some utilities are offering "EV tariff rates" that are cheaper than the normal rate). Assuming you are not on one of these EV tariff programs, then EV charging shows up on your regular bill and it is indistinguishable from your TV or refrigerator's electrical usage. I don't know about your electricity bill, but mine is complicated. There are different rates for different levels of usage, there are distribution charges, connection fees, taxes... Each bill is about 20 items long. But you can simplify things. Just find the total kilowatthours (kWh) used and then find the amount due. From these two you can find final the cost per kWh. Our most recent bill was $173 for 1517 kWh. That is an average of 11.4¢ per kWh.
Once you have the price per kWh, you can figure out the price per mile for an EV. A 2015 Nissan Leaf, for example, has an EPA rating of 3.33 miles per kWh. That works out to 3.4¢ per mile. That is about one third of the 10¢ per mile from the gas example above.
You can think about this way, every $10 you spend on electricity saves you $30 at the pump.
Above we used the simplest method to compute the cost of a kWh. In 2012, we signed up for Portland General Electric's TimeofUse (TOU) program. It's a timeofday based rate system. TOU charges different rates for electricity at different times of the day. They have onpeak, midpeak, and offpeak pricing. Here is the chart from our December 2015 bill.
Timeofuse chart 
Even with gas at $2.50 per gallon, charging an EV at offpeak times can be 73% cheaper than driving a gas car.
I started writing this post because recently there were some questions about TOU from my 2013 post on the topic here. So in the rest of this, I'll break down our December electricity bill in more detail.
Electricity is generally inexpensive here in the Pacific Northwest when compared to places such as southern California. So here, the default program is usually a flat rate (called Basic Charge by PGE). With a flat rate, a kWh costs the same at noon as it does at midnight. As you use more, you may move into a different pricing tier, but the timeofday does not matter.
Here, it only makes sense (and cents) to switch to a TOU program if you can move 50% or more of your usage to offpeak. As you can see in the chart above for December, we were right at the 50% mark.
We shifted our usage in two primary ways. First, we have 12.3 kW of solar panels. This generates electricity during onpeak and midpeak, thereby reducing our grid demand during these times. Second, as discussed above, we have an electric car. The car's charging station is programed to charge the car up from 3 to 6 AM each morning. This fills up the car during the offpeak rate period. We plan on adding a 2nd plugin car to our home fleet soon. This will increase our offpeak usage even more.
The concept of TOU is simple enough, but the impacts to your bill are more complex. The best way to understand it is to examine an actual bill so you can understand how it might save (or not save) you money.
December is a good month to examine since it's one of the worst case months. In the spring and summer, we save about $10 on each bill. In the winter we are close to break even, we may save a little or pay a little extra than we would if we were on the flat rate. Looking at it annual, we save money, so paying a little extra in the winter is no big deal.
So here are the details from our December 2015 bill:
Off Peak Rate  kWh  Subtotal  Adjusted  Adj Subtotal 
$0.04195  761  $31.92  $0.08793  $66.91 
Mid Peak Rate  kWh  Subtotal  Adjusted  Adj Subtotal 
$0.07222  436  $31.49  $0.11820  $51.53 
Peak Rate  kWh  Subtotal  Adjusted  Adj Subtotal 
$0.12581  320  $40.26  $0.17179  $54.97 
I should clarify that adjusted rate (Adj per kWh) is not listed on the bill. I computed this by adding up all the additional charges that are on the bill. There are 16 of them. Most of these are per kWh charges and are easily applied to each rate. A few apply to only the first 1000 kWh and others (like the $10 connection fee) are a fixed amount. To simplify all of this I just prorated all the charges as per kWh. While not 100% accurate, it is close enough and this method accounts for the entire $173 bill. By far the biggest of these adjustment fees was the $60 Distribution Charge. It accounted for 85% of the adjustment amount and it was a per kWh charge.
Here is our list of per kWh adjustments:
per kWh Adjustments  Fee per kWh 
105 Regulatory Adjustments  $0.0006600 
109 Energy Efficiency Funding  $0.0031800 
110 Energy Efficiency Customer  $0.0000700 
122 Renewable Resource  $0.0001800 
123 Decoupling Adjustment  $0.0003400 
137 Solar Payment Option Cost  $0.0004700 
143 Spent Fuel Adjust  $0.0012700 
144 Capital Projects Adjust  $0.0016100 
145 Boardman Decom Adj  $0.0003700 
Transmission Charge 
$0.0024600

Distribution Charge  $0.0392600 
And here is the list of fixed charges or charges that didn't apply to every kWh:
Fixed Rate & Capped kWh Adj  
Basic Fee  $10.00000 
First Block Adjustment  $7.22000 
Low Income Assistance  $0.84000 
Public Purpose Charge  $4.88000 
102 RPA Exchange Credit  $8.55000 
How much would this month have cost with the flat rate? The adjustments and fixed charges are the same on either the TOU or the Basic Rate plan.
Basic Rate 
kWh

Rate

Adjusted

Adj Subtotal

1st MWh  1000  $0.0650  $0.1110  $110.98 
Over 1MWh  517  $0.0722  $0.1182  $61.11 
This adds up to $172, so we would have saved $1 if we were on the flat rate plan. Again, this is more than made up for by our summertime savings. In fact, I'll make this deal with any of you. For every $10 that you give me in July, I'll give you $1 in December :) PGE does not let you switch between the Basic Rate and TOU rate each month. When you sign up for the TOU rate program, it's a one year commitment. So I can't take the $10 in July and then skip out on the $1 in December. The good news is that in the first year on the TOU program they guarantee that your total annual bill will not be more than 10% higher than it would have been with the Basic Rate plan. This way, if TOU is not the great deal that you thought it would be, you can cancel the program after the first year and not be out too much money.
There you have a it, a break down of EV charging cost and the TOU rates and fees on a Portland General Electric bill.