What am I doing wrong? I was introduced to meditation many years ago through a short course and a book. Essentially I tried the mindful breathing meditation. I kept at it for a couple of years after which different circumstances resulted in me forgetting all about the meditation. Maybe it was due to my not noticing any discernable effects. But now I am trying to pick it up again. Currently I am following the book "Wherever you go, there you are" by Jon Kabat-Zinn.
However, I have a few questions: 

1) Everywhere I keep reading stuff of the kind "Observe your thoughts without judgment". What does that really translate into in practice? How do you observe without judging? I mean, if you get sad thoughts, you get sad too. Thats why they are called sad thoughts. I never understood how to actually follow this advise.

2) Again, I keep reading "Observe this particular moment", "be in this moment" etc. What other moment are we normally in? What special tasks do we need to undertake to be in this moment? I mean, as long as you don't daydream about the future or wallow in the past, you're in the moment, right? This is something I again fail to comprehend clearly.

3)"Observe the breath". Do I feel the breath? Or note that I am breathing? Or count the breath? It just feels like more thinking.

4) How do you ever "know" that your meditation is working right? Or how do you even know your practice is headed in the right direction? I got tired after 2 years of it and nothing in return. Okay maybe I did it wrong, but how would it have been had I done it right? Is there a time frame within which you can expect some sort of result if you do it right?

5) There seem to be many kinds of meditations, each with its own set of fanboys. Are these different types simply different paths to the same goal? Or are they meant for different goals? Moreover, are their learning curves different? How do I know what is right for me? Does this analysis even matter at all or am I just complicating things needlessly? My aim is to be able to concentrate and think clearly without getting overwhelmed.

Clearly I am doing it wrong, for I feel no difference. The meditation books are full of hollow cliches and deep-sounding mumbo-jumbo which isn't helping at a practical level.

Just to put the facts out: I am a mathematics grad student deeply interested in algebra and computing, and a Hindu by birth. I find religion and mythology fascinating from a historical perspective though am not spiritual or too keen on the underlying philosophies. I have also faced recurrent issues with OCD and clinical depression and insomnia, but medication, therapy and most importantly, time, have made things better. I am, and have always been curious about meditation, but have not been too successful or consistent with it. I am not opposed to religious imagery or artefacts in the meditation practice, though I'd prefer it to be as objective as possible.

Any advise/suggestions would be great. Thanks!
I think you did a really good job of breaking down your doubts into individual points.


  
    1) Everywhere I keep reading stuff of the kind "Observe your thoughts without judgment". What does that really translate into in practice? How do you observe without judging? I mean, if you get sad thoughts, you get sad too. Thats why they are called sad thoughts. I never understood how to actually follow this advise.
  


In Buddhism we separate the initial thought from the emotion which we apply to it. The thought isn't a bad thing until we start to apply our ideas to it, we call it sadness and we want to get away from it, we start to think of how good life would be if we could avoid sadness. It is only after we apply our ideas that this thought becomes bad.

As humans it's very hard not to see sadness as a bad thing, we cannot immediately control our reactions to avoid labeling sadness as bad. When beginning with meditation we practice allowing the sadness to be present in the mind and not try to get rid of it.


  
    2) Again, I keep reading "Observe this particular moment", "be in this moment" etc. What other moment are we normally in? What special tasks do we need to undertake to be in this moment? I mean, as long as you don't daydream about the future or wallow in the past, you're in the moment, right? This is something I again fail to comprehend clearly.
  


You're right that thoughts about the future and past are not part of the practice but sometimes we get distracted without going to the future or past. For example if we see a bar of chocolate we have sight in the present moment; then we might get distracted and start to think "Where are these chocolates made?" or "How many calories are in the chocolate?". These thoughts aren't about the past or future but we are now lost in thinking and we are not in the present moment.

As an extra note, if you change from seeing chocolate to thinking "How many calories are in the chocolate?" then the present moment changed from sight to this thought about calories, you could remain in the present by observing the thought but observing a thought is different from just thinking it.


  
    3)"Observe the breath". Do I feel the breath? Or note that I am breathing? Or count the breath? It just feels like more thinking.
  


Some of the suggested techniques do involve more thinking than others. One aim of meditation is to reduce the amount we get caught up in thoughts. Just feeling the breath involves less thought than counting the breath, in that way feeling is better than counting. You know from meditating that it is difficult to stay aware of the breathing, some people are so stressed that they have to count their breath, it is too difficult to only feel the breath. For these people counting is a good idea until they are calm enough to just feel the breath.


  
    4) How do you ever "know" that your meditation is working right? Or how do you even know your practice is headed in the right direction? I got tired after 2 years of it and nothing in return. Okay maybe I did it wrong, but how would it have been had I done it right? Is there a time frame within which you can expect some sort of result if you do it right?
  


If you are doing meditation correctly then you should notice an improvement in your reactions to things. Maybe before when a person shouts at you then you get angry and shout at them, after meditating for months when a person shouts at you then you notice your anger and you don't immediately think that you have to shout.


  
    5) There seem to be many kinds of meditations, each with its own set of fanboys. Are these different types simply different paths to the same goal? Or are they meant for different goals? Moreover, are their learning curves different? How do I know what is right for me? Does this analysis even matter at all or am I just complicating things needlessly? My aim is to be able to concentrate and think clearly without getting overwhelmed.
  


Largely the different meditations are different paths to the same goal. Any meditation which involves observing an object (the breath, the body, a coloured disc, a flame) the object is unimportant because eventually in deep meditation you will not be able to see/feel the object. Because breath meditation is so popular there are many many variations of how to watch the breath but you just need to find the one that works best for you. The only way to know what is right for you is to experiment with different types, a month should be long enough to know if you like it. None are perfect so just find one that is good enough for you.

Last bit of advice: Meditation involves letting go of what is happening. If you are trying very hard to follow your breath then you are preventing yourself from being relaxed. Ideally you should not require effort to remain aware of the breathing, you just won't get distracted by other things because you are calm.

I hope that some of these answers help you to develop a fruitful practice.