What are some ways one can improve his/her speed of thinking and reasoning ? I am looking for some easy to follow strategies that can be systematically applied. (I am presuming it can be learnt/ taught ).
I think you need to think about what you mean by "speed of thinking". Your language implies that you are looking for a generalised way to be more intelligent. I have not seen any simple interventions for increasing general intelligence.
You may find it more productive to focus on particular domains of your life that you want to improve. Practice and instruction improve performance in a given domain. There are a wide variety of mechanisms by which this occurs, some of which could be characterised as speed of thinking.
In particular, practice often leads to automaticity. Take for example, learning your times tables. When you first encounter a given question (e.g., 8 * 8 = 64), you may have to use a longer algorithm to solve the problem, but with practice, the equation itself may directly trigger recall. Alternatively, take many computer based tasks. The first time you try to perform a task (e.g., sorting your email by date), you may have to think more about how this task can be performed. With practice, you just recall how to do it. A similar process of automaticity also applies to the perceptual and motor domains as you learn to assign visual attention effectively or learn to smooth out motor responses (for a review see Rosenbaum et al 2001).
This process of acquiring automaticity in a given domain is not exactly speed of thinking, but it has the same consequences. Automated actions reduce the demands on limited attentional resources, and can be executed quickly and efficiently.
For specific suggestions on what makes a great practice schedule you may want to read up on the literature on deliberate practice (e.g., Ericsson, et al 1993).
In chess it helps not to watch for the entire thing, instead to watch only out for "structures" you know, e.g., some particular structure of a famous checkmate position.
You can also think in layers, and remove minor threads out of your thinking, like pawns or pieces on the starting line. This should also work in real world thinking.