Centering takes a lot of time and patience so dont worry about concentrating on it too much as we all have everyday work to do and it is hard work trying to blend all that together early on, it will come with time and practice so dont worry! I'll try and explain a bit about how it should work to try and help give you an understanding, but its based on my own experience with centre, there are many people that can help explain what centre is and have different ways of achieving a good centre, but only you can find out for yourself what it feels like, learning about centre is a journey, so my explanations may appear a little vague or "over your head" to you and theres only so much i can type out on this thread unfortunately to try and describe it. Here it goes anyway!
Its important that to fully realise centre you should try relax into it, this takes a long time to master and that means taking time to relax and settle into centre as much as possible in daily life, even if you just try it a little to start with it in your spare time, a little soon amounts up to a lot. The easiest way i find to settle into centre is to try focusing and settling into it standing in shizentai (natural stance) and breathing from centre, in through the nose to centre and out through the mouth from centre, feeling centre rise and fall. Standing is the bodies most natural state for finding balance and helps to align the body properly and naturally for settling into centre. Breathing from centre is important and the ki that is taken in from your breath will help to build centre (which is ki) and also help develop breath power (Kokyu) which comes from centre, so its important to breath lightly and effortless without any force from your dantien (centre) to begin with until a strong centre is developed, ki is very subtle and linked with breath so this takes time and a lot of practice and patience to develop, but you will notice a huge difference in how this helps you develop your posture, technique and your natural flow of ki and how you move. You will feel more stable and grounded, balanced yet alert and free'er, you will also feel a lot calmer and harmonious and less tense. This grounding effect will enhance your technique and feel from centre as well as your feel of ki. All movement and technique should come from centre and also everything you do in daily life, whether walking, sitting, standing up, going to bed, doing the dishes ect, its not just for the mat. You may also develop a small pot belly around centre but this is just the bodies natural way of settling properly around centre as nature intended instead of living hunched up and tense in the head and shoulders (a sign of ego, tension and being off-balance), its only natural to keep the weight underside and centred and is a basic principle in aikido, without proper centre aikido cannot be performed properly. O'sensei Morihei Ueshiba spent years training and developing his centre prior to Aikido and it was the realisation of a true centre that gave him the insight to develop aikido, the principle of a true centre is called "nen" which is the complete co-ordination between mind-body-spirit at the centre and at this stage one actually becomes and exists as
centre, which gives birth to supernatural power, this is the link to enlightement and true harmony which is the goal of aikido and the purpose of training. Aikido is much more than just learning the physical martial technique although the physical techniques and posturing will help you get a basic grounding for centre in the early stages, principle and technique come hand in hand and should be in harmony and that means giving and existing from centre, its only through proper centre that correct waza (technique) can be performed and it will continually transform your life. Once "nen" is achieved, technique becomes natural and from "nen" you will be able to perceive the imbalance of everything around you because you are so balanced and it will increase your awareness (zanshin). O'sensei used to say that you should "stand on the floating bridge between heaven and earth".
It takes a lot of trial and error to find it, so dont beat yourself up if you find yourself struggling, nobody can find it for you and its something that you have to learn for yourself, but its fun trying and its good to keep a positive frame of mind, it will take a while to get it, but you will get there, you get back what you put in! Just remember that everything should come from centre, move from centre, breathe from centre, technique from centre. Even ken and jo waza should link from centre, even the way you drink your beer.
Meditation is also good for developing centre, in fact centering is a meditation, but meditation is not in the act of trying to meditate, that is technique, it is what lies beyond the meditation that is "meditation", true centre "nen" works in the same way, when everything comes together in harmony (mind/body/spirit) is co-ordinated at the centre and you then become "nen", its when you reach that stage that all your single minded focus on your centre disappears naturally, "nen" takes over at this point and does the work for you, you are then simply functioning within the laws of nature, which protects you and opens a whole new world to you and fills you with love and wisdom.
There is a nice little chapter on the basics of practicing centre in a book called "Aikido in every day life" by Terry Dobson and Victor Miller. It gives a nice and easy way to understand what your trying to achieve from the very beginning and gives you some simple exercises to try and help you with your centre development, as most books dont really give you an in depth idea of what it is, is worth a read!
Good luck and happy centering!