What's the best way to get rid of my nasolabial folds that I've had since I was a child? (Photo)

I would start with fillers in your case. I think you will get okay, but not excellent results, mainly because your nasolabial lines have a mimetic component for which Botox would not be a safe option and which filler wouldn't fully deal with. Review your case in person with an expert injector (e.g. dermatologist) who can provide you optimal results (ie. natural look) and safety, and honest expectations.

This is a very common area of concern.  Based on your photo you have strong nasolabial folds and smile lines or parenthesis lines.  Please remember that every child has nasolabial folds - they are natural, to a certain extend.  You will need to consult with you provider and assess your lines during different expressions. 
The are so many treatments available to significantly improve your concern.  Fillers are the most common starting point, very safe in expert hands, and not permanent.  Your provider will take into account the other features of your face when making recommendations.