There really isn't a simple answer to this question.
As there are many different styles of calligraphy around the world there are also many different tools used to create these styles. In the general sense though most calligraphy is written using a nib, pen holder and ink. It is the nib that is the most important factor in creating different styles. There are two main categories of nibs, pointed pen and broad nib, and they each have their own characteristics.
POINTED PEN CALLIGRAPHY
Pointed pen nibs can be used for more traditional styles of calligraphy such as Copperplate or Roundhand and also for Modern Calligraphy styles. This calligraphy style is based on the amount of pressure you apply when writing. You will notice that there are thick downstrokes which are made by applying more pressure and fine upstrokes which are made by releasing nearly all of the pressure.
There are many brands of nibs for calligraphers to choose from. Each one has different characterics/personalities and what works for one person doesn't necessarily work for another. My go to nib is the Nikko G nib as I find I apply quite a lot of pressure when I write and having a stiff nib suits this. Definitely don't limit yourself to just one type of nib though as you will find some projects call for a more/less flexible or finer/fatter nib.
It is quite difficult to write large letters and letters with super thick downstrokes using a pointed pen nib. If this is what you want to acheive I would suggest trying a brush instead.
An oblique pen holder is most commonly used with pointed pen nibs as pointed pen calligraphy is written on a large angle and the oblique holder helps to reduce the amount you have to twist your hand. The pen holders can come in wooden or plastic varietys. I prefer the wooden holders so much more though! My favourite is my rose gold wood holder as the finish is very smooth and the colour is so pretty!
BROAD NIB CALLIGRAPHY
I must admit I have only worked with one variety of broad nibs, which is the Speedball C series, as it was recommended at my first ever calligraphy class. It comes in sizes 0 - 6, six being the smallest. There are other similar nibs but as I haven't had any problems with Speedball ones, I haven't had a reason to try the others!
Broad nibs are used for hands such as Italic, Gothic, Uncial, Byzantine etc. - generally the more square calligraphy styles. The edge of the nib is usually placed at an angle which is how the thicker and thinner lines are created. You can get a variety of line widths by using different sized nibs. The wider the nibs, the larger you write your letters as the proportions of the letters always stays the same. In the speedball range, size 0 produces the largest sized letters. If used correctly broad nibs always produce a consistent application of ink.
Broad nibs are always used in conjunction with straight pen holders because the angle of the letters are more vertical than pointed pen calligraphy. The straight pen holders are more commonly found in stationery stores compared to oblique holders.
OTHER WRITING INSTRUMENTS FOR BROAD NIB STYLE CALLIGRAPHY
Pilot Parallel Pens
Parallel pens are basically a broad edge nib and holder made into a pen which holds the ink. This is amazing becuase you don't have to dip into ink all of the time. They come in eight different widths and you can even find customised ones which produce interesting effects. You are limited to the ink colours they produce but there is a nice variety of bright colours. The pens are also great for travel or when you're on the go.
Automatic pens are holders with different fixed nib attachments. They are generally either super wide nibs or nibs that produce two - five lines at once. The five line nib was firstly used for writing music. These are perfect for creating interesting effects.
Balsa wood is a very inexpensive option for creating larger, thicker calligraphy. You can cut it to any size you want and it creates really nice textures dpending on how much ink/paint you put on the wood.
The article you have just read is only a very quick introduction to calligraphy tools. It can often be quite the balancing act making sure that the nib, holder and ink all work together to produce a great result. Calligraphy is a skill that requires a lot of regular practice to get better and I feel it is impossible to ever know it all. You can have a lot of fun trying to learn it all along the way though!