Thank you for sharing you Question and great job on having the determination to start your personal practice!
The first tip I would provide to you would be to seek out Meditation Centers in your area where you can learn from a true Meditation Teacher - their advice will be very valuable to you as you may have many questions.
You can easily Google "Meditation" in your city and you should find a few centers to try out - search for a Modern Meditation or contemporary meditation group if you would like to have it be religious dogma free. Mindfulness based meditation is one that has been primarily brought forward by Dr. Jon Kabat-Zinn and is a good start as well - you can find a guided audio meditation download to start your practice off on my blog site.
Be careful to fall into one technique of meditation - there are over 155 commonly practiced types of meditation so seek out a few, practice each for at least a month, and make the choice of which one works for you best (keeps you motivated and happy to do it)
Also a difficulty that might arise is an association to approaching meditation as a state of "not thinking" - it can raise much difficulty as you will be battling the surge of thoughts that will naturally arise.
Have a mindset to one where you "are not suppressing or represssing thoughts" this way these thoughts will help you deepen the meditative state - allow them to rise and congratulate yourself when a thought comes to your awareness, then gently bring your attention back to the stillness of your body and subtleties of your breath.
Most importantly be playful and be patient! Meditation is essentially connecting with the present moment, entering a state of feeling and silent watching of everything that is happening within you and around you - the more you do it the more heightened your Self-Awareness becomes.
Here are a few Introductory tips I provide for my Guided Audio Meditations:
1. Make sure to dedicate about 30 minutes in a silent room, with phones, alarms and other notifications turned off - take however much time to meditate that is comfortable though aim for a number that ends with 5 and set a timer to help guide you (10, 15, 20, etc. this way it helps you try to extend the practice)
2. Have a tea and take care of any other necessities prior to your practice
3. Dress Comfortably
4. Find a comfortable seated Meditative Position- making sure to have your back straight, chin parallel to the floor and your stomach relaxed (billow it out and embelish the curve in your lower back).
5. Be playful, patient and let go of any sense of “attaining” a certain state – be compassionate to your self throughout this practice.