Any woman loves details, little displays of affection, unexpected behaviors that make clear something has reminded you of her, that she is in your mind, that you would like to do things with her. Singles trying to establish a relationship through online dating websites would do well to remember this, because it will help them succeed.
Of course, not all women are the same, but most love their partner or the guy who hopes to earn that title to give them small gifts. These must not necessarily be purchased items: what is more important is the time/effort you put into it, and the intention guessed behind your gesture. The simple fact of taking the time to plan something for you to do together is a present, and they might value it over the planned activity itself!
If contact with your dream single woman is still limited to Live chat or phone calls, you can score some points by sending or mentioning a sentence (a quote, a song verse, etc.), and tell her why it reminded you of her. Another possibility is sending a surprise email with a link, a sound file or an image of something she might enjoy (e.g. a link to one of her favorite artists video). You can also pay compliments, hopefully with some originality, and always-always-always rise to the occasion when you are given the chance to act gentlemanly: this never goes out of fashion. In any case, during the first phase of the relationship you would better behave discreetly and moderately, so as to avoid intruding or appearing invasive.
Once you are in friendly terms and contact is frequent, at that point where signs of evident reciprocal interest have been exchanged and emotions seem to be gaining ground, you can move forward a bit. Maybe you have not met yet, so best keep to the same line, but with more dedication on your part. We all have a creative disposition; for you it could be music, photography, arts & crafts, writing, etc., so why not to take advantage of it?
That single woman would probably love to receive a song composed by you, an artistic or downright fun picture you made or that portraits you in a positive light, a Pinterest board with images reflecting what you know and guess about her, a virtual postcard with a brief note showing your feelings, an email with a funny childhood anecdote, a family recipe, etc.
When things seem to work nicely after some dates in the real world, you can go for physical objects or things that require more time/planning/skill. For instance, a collage or mini scrapbook about the relationship up to now, starting with your online dating website profile pictures and a few key messages exchanged there, something that reminds you of the first calls, mementos from the first date, meaningful anecdotes to share and preserve e.g. it is likely you have surprised each other at some point, etc
There are many possibilities, considering your skills, preferences (and hers!) and the chances that come up: a plant you have grown, a poem, a home-made cake if you go on a picnic... The thing is to remember showing these gestures of appreciation and love now and then.