Could anyone let me know if this could be done using LaTeX? And if so, how do we do that?

Could anyone let me know if this could be done using LaTeX? And if so, how do we do that?

I don’t think that this image is created by using a digital font. It seems to be hand drawn, since there are so many different forms of the same characters, e.g. compare the very different e, i, m t or s forms:

So the answer to your question is: No it can’t be done with TeX since there is no adequate font for this.
To do something like this, I guess, TeX isn’t the right approche … a vector based image software, like Inkscape or Adobe Illustrator, will do a better job on this … after drawing it in Inkskape one may export the image to TikZ and use this code in a TeX document or simply include an image file (PDF, JPG etc.).
If you find a calligraphy font that looks like you want, it would certanliy be possible to use it with XeTeX, or even PDFLaTeX, but it could be very hard to handle all the ligatures / joins between letters and the positioning so even with a nice font I would rather use Inkscape/Illustrator.
fontspec's documentation)? Though it is unlikely, it would be possible to create a font with that many variations (Zapfino has 7 or so). They are defined as unicode ligatures, but you can select/switch them by hand if you want.
– ienissei
Mar 31 '13 at 17:47
As others have pointed out, you need a calligraphic fonts with such features. One such font is Zapfino. Zapfino has different shapes for the same letter, as seen from the Wikipedia image below that shows different foms of e in the font.

You can use xetex or luatex engine to use this font. You'll have to activate specific font features to get the desired effect. For example, see Chapter XII of ConTeXt - History of LuaTeX manual. Below is an image from the manual (notice the different shapes of p, g, f, and h)

Related to your engine (pdfLateX, LuaLaTeX, XeLaTeX) you have the following options:
Using this engine means that fonts need special handling. Some fonts are available via packages. Documentations like fntguide or fontinst describe the usage of new fonts and the installation. The process isn't simple. The easiest way is the usage of a installed font. A list of fonts are in the Font catalogue which has a separate section about Calligraphy
These new engines provide a new implementation of fonts. Every otf-font can be used directly. The simplest way of using such fonts are given by the package fontspec.
More information about these engine are provided here:
xelatexorlualatexbut perhaps if you can download the font, then they can be used through the packagefontspec. – hpesoj626 Mar 31 '13 at 09:07xelatexorlaulatex. – Stephan Lukasczyk Mar 31 '13 at 09:10