Love the question!
You should of course realize that it is extremely expensive to transport water. There's a whole science dedicated to extracting water from food, just to make its transport viable. So your question should really read: "what is the cheapest way to melt an iceberg and transport the molten water to the areas in need of it? How much initial investment, maintenance cost and profit margin will make this endeavour economically viable?"
Knowing what I know, I think it's a fair bet that no matter what you do, you'll always end up with negative profit margins, in other words, losses, in other words: it's not economically feasible unless backed or even initiated by government.
Anyway, my initial brain farts on the technical parts of the problem:
You could hack off pieces from the top and lay the pieces to defrost in the Sun. The iceberg would gradually float more and more upward, because at any point physics will guarantee that a certain percentage will be above the waterline.
Advantages: You'd have pretty direct results, and the size of the pieces coming off can be controlled. You don't need to develop new equipment, simple cranes and drills etc. will do. Provides reasonable amount of permanent jobs.
Obstacles: you'd have more melt losses, because of the amount of time it takes to hack away millions of tonnes of ice. You'd have to create and operate machinery to do the hacking, which makes the water overall more expensive, and have a large CO2 footprint.
You could tug it into a sluice -- a body of water that can be completely sealed off from the ocean. Once there, seal the region, and pump all the salt water surrounding the iceberg back into the ocean. Once drained, let the Sun do its work, and pump all the fresh water to its destination.
Advantages: relatively small CO2 footprint, because the process is mostly passive. All the pumping can be done with renewable energy sources, and you'll have little additional losses. Provides enormous amount of construction jobs during initial stages.
Obstacles: the doors to the sluice! They'd need to be as large and strong as a dam. And movable, no less -- way too expensive, unless you have all sorts of geographical advantages to help you. Therefore, provides enormous amount of jobs during construction phase, but these jobs evaporate nearly all when entering maintenance phase. Also, it can take ages before enough water has been molten off and pumping to the transport system can begin.
Instead of hacking from the top, drill a hole to the centre and fill the central region with powerful cold gas explosives. The iceberg will break up in smaller, more manageable pieces. Lift the smallest ones onto land with overhead cranes and let them melt in the Sun. Repeat the process for pieces too large to lift, or simply wait until they can be lifted.
Advantages: Pretty direct results. Provides large number of permanent jobs.
Obstacles: potentially large losses due to smaller pieces melting more quickly, and/or pieces broken off are too large to lift and too small to use explosives. You'll have to have specialized equipment (re-usable cold gas explosives, overhead heavy-lift cranes with "ice-capturing arms", drills, etc.) which can be expensive in maintenance.
Blow hot steam/air onto a fairly narrow region on the top of the iceberg. A small pond will result. When the pond is large enough, start pumping out the water onto the transport. Continue the process, possibly by moving the steam blowers position to optimize the iceberg's melt process.
Advantages: Very fast and direct results. Easy to operate. Using geothermal energy, it'll be low on CO2 emissions and ocean water can be used to generate the steam/air.
Obstacles: if you're lucky enough to be on a thin layer of Earth crust you could use geothermal energy for it, otherwise, the water will likely be too expensive due to energy requirements and large CO2 footprint. Even so, when using ocean water for steam, maintenance can be a problem due to the salt buildup. Also this method does not provide many permanent jobs. Also, it will give rise to additional losses due to the hot steam evaporating the potable water. Also, the last parts of the iceberg will be hard to melt and pump -- these will be lost.
I'd imagine a net of pipes connected to a main pumping station, with smaller ones where needed on important nodes in the network. The main pumping station will be connected to the pool where all the smaller pieces are being molten by the Sun.
Advantages: well, clean water coming from an actual tap.
Disadvantages: This is expensive infrastructure. It's fairly easy to maintain, but the initial cost of construction can be prohibitive. Provides jobs only during initial construction, most jobs disappear when entering maintenance phase. Also has limited range.
Trucks. Load the water onto trucks and transport to needy areas. If you have railroad, use that first to cover the larger distances.
Advantages: simple, existing, cheap, reliable method of transportation. Provides permanent jobs. Can get water to places that are hard to reach otherwise.
Disadvantages: you'll need a lot of trucks; large CO2 footprint.