How can I make a homemade latte taste like a restaurant one?

I find that the milk/foam is the thing that makes all the difference. Most of the domestic coffee machines make a poor job of frothing the milk for Lattes and cappuccinos. I use a steel milk frothing pan like this one:

http://www.saltandpepper.co.uk/cook_shop/brand/Judge/Milk+Preparation,195/2507

I bought mine in Italy 10 years or so ago but I have seen them on our high street since then. It goes on your hob where the milk, UHT or Semi skimmed seems to give the best foam, is heated till it is hot but not boiling and then you use the hand pump to force air through the hot milk and make it thick and foamy, this takes about 15 seconds. I then sugar my black espresso and pour it through the milk to make latte.

You didn't say in what way your coffee didn't taste the same, however, here are some of my thoughts.

1. Is this the same brand and type of coffee as at the shop. Different beans can have distinct different tastes.

2. How fresh is the grind? Coffee loses some flavour if stored ground.

3. How coarse is the grind? When you bought your coffee, did you tell the shop what machine you were using? Different preparation methods use a different coarseness of grind. Obviously, buying a machine that grinds itself will solve this as well as point 2 above.

4. How good is your machine? Some machines just make a better cup than others. If you can borrow a friends machine and try your coffee/method with their machine and see if that makes a difference or not.

5. Container. Some containers do make a difference. Personally I can't stand Styrofoam cups for coffee.

To answer your question with a straightforward solution, my key recommendation would be to buy a new machine for two reasons: better espresso and milk.

Before all, if you are not willing to invest more than $100 (USD) in a machine (more like $350, but I'm sure you can scrounge for a decent entry-level machine to get the job done), you can stop reading as my suggestion relies on a better machine. That said, quickly browsing Amazon I found a Cuisinart unit with tepid reviews (205 averaging 3.5 stars) on sale for about $80.

Here is what is going wrong with your latte:

• Machine: If you have a Krups it's pressure probably isn't rated. This is a bad sign as it indicates how well it will "pull" (brew, make) the espresso. My guess for most units: Unrated = won't pull. Buy a machine with a rated pressure, 15-bar is what to expect. (I don't mean to sound snobby; I got by with a $60 Coffeemate for awhile, but they won't get you the results you're asking for)
• Bean: Lattes are made with espresso, not coffee (U.S.). You're using coffee. So start by buying espresso beans instead of dark roast coffee or Folgers. While you're at it, if you want it to taste like restaurant quality, buy them from a local roaster (I'd imagine you can get some mad fresh beans in Africa) and grind them fresh (just prior to brewing). I prefer a coarser grind to my espresso, you will also need to press the grinds ("pack") in the gruppa (metal basket of machine).
• Milk: While you're at it, don't necessarily use whatever comes out of the fridge. Here and here have the dirt on milk and frothing. Basically fuller body for the drink use milk with more fat, if not use less fat. If you have a favorite place in mind for your exemplar latte, go ask them where they get their milk and follow suit. There's a degree of preference in which milk you use, go with the one you know you prefer and perfect your technique.
• Frothing/Steaming: You aren't frothing your milk. Buy a machine with a working wand, froth the milk. Actually, frothing the milk is fun and it tastes great all on its own. Note: you do want to get foam on top, this indicates you have properly steamed the milk below (remember to hold back the foam, and pour only the steamed milk into your latte, then depending on your region's definition adding a bit of foam on top).
• Container: Add some dignity to life whenever you can. Use ceramic; you're at home.

Those are the key differences that are causing problems for the latte you want to amp up. Now you can skip the consumer espresso machine advice and get a stove-top setup (espresso pot and use a normal, smallish pot with a whisk for the milk), but that takes a smidge more effort in terms of getting it right. Either way, following these guidelines should get that latte much closer to where you want it to be. Basically, the only advantage the shop will have over yours is a bigger machine, overworked employees who might not have the time to care about your coffee at this time, and paper cups.

Simple, you get a high end domestic machine and learn how to use it. These simply contain similar hardware to your dual or triple group head cafe machines.

The cheapest machine that you can get - you mentioned lattes so you need to froth your milk - is the Rancillio Silvia. This is quite popular so you should have no trouble sourcing one. Also very important is your grinder. Ground beans go stale quickly so you need to G.O.D. Grind on demand.

Expect to part with $1000+ to get started.

So why does this differ from your Krups which kinda has similar looking parts? First the espresso shot. We are grinding coffee fresh, to a finer grind, using more of it (approx 7 grams for a single shot) and extracting under pressure. Extraction is probably less than 30 seconds. What we are trying to achieve is to extract only the good bits and leave the bad bits.

Once you have perfected that you have to steam your milk. With a good machine, you'll be able to create micro-foam which is tiny imperceptible bubbles mixed into the milk. This is easiest to achieve with full cream milk. The texture of the milk will be like cream. This is kinda like CO2 in fizzy drinks. It changes the mouth feel and makes the milk taste a bit sweeter.

These bubbles will start to separate eventually. So done correctly, you should be able to pour the milk straight into your cup and after a few seconds the bubbles separate to give you your distinctive layer.

You'll be able to get a great result with a plastic cup to take with you, but when at home, warm your cups on the top of the machine.