Although i have written this in the sense of awakening a Goddess statue so as not to go back and forth between male and female this is the exact same process for any God you may be working with.
Every statue made in the likeness of a Goddess holds a little of Her essence however if you want to invite Her into your home, sacred space or life there are ways in which you can make your request known to Her and 'awaken' the statue in Her name so She has a vessel to reside in.
First place your statue in the area you have set aside for Her, it does not need to be large and can be on your general altar or a kitchen shelf (Hestia for example) or fireplace mantle (Brighid) etc. You can now smudge and if part of your practice cast circle.
Then place an offering next to the statue, maybe some gemstones which resonate with that Goddess, food, flowers, honey and a candle you can light regularly.
Choose an incense which again is favorable to that Goddess and let the smoke swirl around the statue clockwise while you invite the Goddess by name into your home and her statue. You can sing, chant, say a prayer or verse or just talk gently to the Goddess here. Go with what feels write and natural to you, you can even dace should you want!
If the statue wont be damaged you can also anoint the statue's feet, arms and forehead using your finger tips with a little of an oil blended specially. During anointing i like to chant the Goddesses name to raise energy and then direct it into her statue (again you can continue with your singing etc as above). I personally always like a working statue i can annoint as part of my practice and then i have other decorative statues. Trust your intuition and remember do not anoint anything that could be stained or spoilt unless you are happy to dedicate that statue for the purpose.
Once you feel energy has built and you can feel the Goddesses presence you can give thanks, close circle if you opened one and carry on with your day. I personally like to take some extra time to meditate and connect, if your Goddess has a temple then visit it, journey to her well. This is a great time to talk to the Goddess and receive any messages She has for you.
Light your candle regularly and repeat the incense and anointing every so often. You can also meditate in front of your statue or do ritual work involving that Goddess. Remember the more time and effort you put into spending with the Goddess the more your relationship will grow )o(