If you can't be mindful while doing NOTHING, how can you expect to be mindful while doing ANYTHING?
Meditation is an opportunity to release ourselves from our habits and fixations, to clear away all the baggage and noise. Meditation is an opportunity to see things, not the way we want them to be, nor the way they were, nor the way we wish they weren't, but as they ARE right now. Meditation is an opportunity to breathe.
There are many ways to meditate, but the way I've always meditated since I was a pre-teen (which is probably Zen in origin) is to "catch and release" thoughts. Find a peaceful place and allow yourself 15 minutes to just sit. You may come in and out of your meditation as often as you'd like. There is no pressure. With practice, you will be able to lengthen your time in meditation and deepen your level of mindfulness, but striving for such things will make it harder to attain.
Begin by sitting in seiza, cross-legged, half-lotus, or full-lotus position, or in a chair. Establish good posture. Be grounded. Be comfortable.
Notice your position. Notice your muscles - many may be contracted unknowingly (like your traps and jaw). Notice the position of your shoulders (which are very likely shrugged). Notice the position of your tongue (which is very likely glued to the roof of your mouth). Relax them.
Notice your breathing. Are you "chest-breathing"? Allow the abdomen to relax and belly-breathe as you would naturally while unstressed or sleeping. Close the eyelids or leave them half-open and focus on nothing in particular.
If a thought or emotion arises, acknowledge it and let it go and focus on the breath. The point is NOT to ignore or repress or deny anything. The point is to NOT attach to anything. Don't fuel thoughts and emotions with further thought and emotional reaction. Allow thoughts and emotions to arise and dissipate naturally.
Reconnect with your breathing.
If you are bored or falling asleep, then you are not in the moment - you attached to a feeling of boredom or fatigue and marinating in it either by fighting it or by being carried away with it. Notice the fatique and acknowledge the boredom, but do not allow it to become more than that. Like all things, like thoughts and emotions, it will ebb and flow, rise and fall, acknowledge this without attaching to it.
Return to your breathing.
As sounds and outward stimuli reach you, do not try to ignore them. Do not be frustrated because you think they are an "intrusion" - they are not. Acknowledge them as you continue your breathing.
If you feel an itch arising, the knee-jerk Pavlonian reaction is to scratch it. We may scratch it if we choose to, but we do it mindfully.
Return to the breath.
If you notice frustration or impatience rising, acknowledge it. Be aware of it but do not dialogue with it.