Illustrator is essential if you want to be professional. You can design with other things, but Illustrator will be demanded by so many clients that you'd be wasting your time as a designer if you didn't have it. You can get Illustrator CS2 and the rest of CS2 for free right now from Adobe's website. If you get good with it, and the situation demands it, you might consider getting CS6.
However, first of all you should establish that you're actually good at designing icons. I don't know anyone who just designs icons for a living, and if those people exist then they must be very rare. Logo design is commonly just one part of designing a corporate identity, which is a broader thing. You ought to be able to do this with pencil and paper, and often that's where logos begin before being scanned, reworked and vectorised. Compare your work with other people as much as possible: [link][link]
The only way is to study and study more. You can buy some books about the process in making a logo, that includes the brief, the color theory, the semantic and morfologic analysis as well the different types of typography. And then practice on paper and later on a vector program.
it's all about the idea and what the logo communicates, aswell as readability. you want it to read in all sizes, and in black&white. you also want them to be very unique and distinguishable. that's why high tier logos are kept rather simple and clear and don't overdo the use of color or symbolism. the execution of the final idea, which like some already said is almost always done in adobe illustrator (you want a vector file), is really just the very last 1% of the work. the 99% before that is purely mindwork and research.
this is not the best example but it should give you the right idea [link]
if you want to work in branding and corporate design (very fun field) you might want to look into studying viscom or graphic design.
It would actually be more important to learn graphic design theory and practices. You can design a good logo on paper. In truth when I design logos I rarely do all the work on computer, I design it by hand on grid paper and just trace it in.
I would like to suggest checking out Inkscape for graphic design. It's a fantastic vector graphics editor with many similarities to Adobe Illustrator. It's used by many professionals in art and game development as well, and it's currently my personal favorite graphics editor to use. Oh, and best of all, it's completely FREE and open source.
There is a bit of a learning curve, as is the case with many unfamiliar graphics editors, but it's definitely worth learning. Check out some YouTube videos regarding Inkscape to get a better understanding of what can be achieved by using this program and also search for tutorials as there are several helpful ones online.
I recommend using a good program, along with taking a few art class geared towards 2D/3D design, and illustration course which are available at most colleges, or if you want to teach yourself use Youtube, or find some videos online to show you a few basics then just play around on your own. You sort of have to be able to sketch out ideas on a piece of paper to show someone AND be able to recreate the same design online. It's really not one or the other. It's both.
Go to university for graphic design? Honestly I've never seen enough resources online to learn this type of thing for free, at least nothing comporable to what I got taught. Though technically speaking you could probably self learn it if you studied enough and had a knack for it. It would probably just take longer.
Pfft. I work as a professional graphic designer. I have a Bachelor majoring in graphic design. Most of the design I do is for work and so is not available online. However I do occasionally do it for my hobbies. I did this one [link], and this [link]. I have some stuff from a couple years back as well, so you didn't look very hard. So tell me again how I don't know what I'm talking about.
You'll find that most graphic designers working professionally that command any sort of decent wage have some sort of qualification. It took me three years to even begin to grasp what it was all about. It's a lot more complex than just making something that looks pretty. There is the theory, such as the study of semiotics and the work of Saussure, there is the technical, understanding the programs and printing, and there is the creative, learning how to be be creative on tap. So if you are serious, study should be in the cards somewhere.
If you want to start by yourself, you'll need to start looking at those three areas.
Start studying design history. Understand communication models between origin and receiver, look at Saussure and semiotics.
You'll need to understand Adobe software. The three main ones you'll need to know are Illustrator, Photoshop and InDesign. These are the industry standard and you'll have to be able to use them in order to work at any work place as a designer. You should be able to get your hands on CS2 now, so start there. Look up on how printing vs web works. Understand CMYK, RGB, DPI and printing specs.
Finally, do briefs. You can find them online or create your own, such as making a brand for a cafe, making a music brand, making a wine brand. This is made up of these stages: Research, Ideation, Development, Refinement. Research is the most important aspect. Study as many designs as you can, but also study everything related to what you are doing. Blogs like this can be great sources: [link]. Ideation is where you are expected to come up with hundreds of logo ideas. The idea is to put absolutely everything on paper. Development happens when you start sorting through the ideas and developing a few to see which ones have potential. The final stage is where you truly refine 1-3 ideas into a clean form. From there you should be able to build up entire brands by selecting colours, typefaces, paper stock etc and apply it to a range of relevant products.
You should be able to draw a few sketches of the logo ideas so your clients will be able to choose which one they like best or ones that they can mix-and-match from the sketches. After, use the Illustrator to draw them.
Hand sketches are for your clients so they can choose what they want finalized. If you're going to hand them finished versions of logos, then you'll tire yourself out. Unless, you don't mind doing that.
Making logos has very little to do with the program you use in the end. It's all about creating a simple, strong mark that communicates a company's core ideals and purpose - whether you finalize the mark in illustrator, corel draw, or any other vector program makes little difference. Take a look at getting David Airey's "Logo Design Love" book: [link]