You profit because the value of the contract will increase with increase in price of the underlying asset (a share in this case) and you sell the contract before you have to actually execute it.
Immediate Pricing Analysis
Let's examine the current pricing of some of call options available right now for Ford stock. What if you buy your contract, then you buy your shares 100 shares at the strike price and you sell them immediately on the open market at $10.78 per share.
Contract Price $5.45 $0.85 $0.43 $0.15
Contract Cost x100 $545.00 $85.00 $43.00 $15.00
Strike Price $5.50 $10.00 $10.50 $11.00
Share Cost x100 $550.00 $1,000.00 $1,050.00 $1,100.00
Buy 100 shares $1,095.00 $1,085.00 $1,093.00 $1,115.00
Sale 100 shares $1,078.00 $1,078.00 $1,078.00 $1,078.00
Profit(Loss) ($17.00) ($7.00) ($15.00) ($37.00)
So right now the contracts are priced such that you'll lose money if you could simply transact, this is normal. In this situation where the underlying asset is about $10 and the contracts are priced in pennies, the variance in the result is largely due to the low cost of the contracts, if you were looking at options for Apple the variance will be much lower, but there it is.
Note the $11 strike contract, the loss widens noticeably when you go "out of the money" so this option carries an immediate loss of $37 because your strike price is out of the money by $0.22 ($11 strike price - $10.78 share price). Taking this in to account there's a loss of $15 ($37 - $22) which is in line with the immediate loss priced in to the other option contracts.
Where is the profit?
So how do you make money trading options contracts? So let's say you buy the $11 strike option priced at $0.15 for $15. Fast forward a few weeks and Hooray, the price of F is $12 when your contract is ready to exercise.
Contract Price $0.15
Contract Cost $15.00
Strike Price $11.00
Share Cost $1,100.00
Total Cost $1,115.00
Sale 100 shares $1,200.00
Your profit is $85 on your investment of $15 which is a return of +467%.
But, to your point, what if you just want to transact the contract. If a share of F is currently trading at $12, an option to buy at $11 will have that $1 profit per share accounted for in it's price. Theoretically at a share price of $12, the $11 strike contract will be priced at about $1 per share (plus a little to account for costs, as illustrated in the table above). So simply looking at the price change in the value of the contract it looks something like this:
Strike Price $11.00
Buy Cost $0.15 x 100 = $15.00
Sell Price $1.00 x 100 = $100.00
Profit $100 - $15 = $85.00
So just like the example above your profit should be just about the same $85. Also just like above when we looked at the immediate transactability of the various options, as in the example of the $5.50, $10 and $10.50 strike prices the detla between the strike price and the current price was present in the price of the contract, the contract will have the $1 of profit built in to the price.
So why options?
Had you just bought 100 shares of Ford for $11 per share you would have an investment of $1,100. That's very different from your investment of $15. Had you then sold at a price of $12, you'd make $100 ($1,200 - $1,100) for a gain of 9%; again a lot different than the gain of 467%. You get 100x the exposure. But what if you have a strike price of $11 and the value of a share of F on the day of expiration is $10.78, your contract is worth $0. That's a loss of 100%, you lost $15 on your $15 and have nothing to show for it. Had you bought the shares your position would be worth $1,078 for a paper loss of 2%. Your 100x exposure comes at a cost and much higher likelihood of total loss.
I hope this helps to clarify how options works. It's good that you're learning about this before blindly putting up money.