I still remember the first time I saw a blooming wisteria draped over a structure. There was a beauty in those hanging clusters of fragrant flowers that took my breath away. I don't remember the first time I saw a briar full of twisted grape vines. I do know that it was as unattractive that day as I find a mess of vines today. Vines have the potential to be the gorgeous, romantic plants or the mess. It is all up to how you work with them.
Pruning/training your vine
To keep any vine in good shape and growing where you want, it is important to train and prune it. Individual tendrils and vines can be wound around the appropriate support devices. If they cannot be unwound from where you don't want them, those vines can be cut off and removed. Many vines respond very well to pruning producing new growth in response. Some vines can even been kept in shape with a hedge trimmer. Remember to look up the information about your specific vine.
Think about the scale of your vine
While pruning will always be a part of good vine care, you also want to make sure to select a vine that works well with your space and your needs. A very aggressive vine like a Rangoon creeper or a wisteria would not be the best for a small trellis in a courtyard. Many blooming vines will not do well in the shade, and you may want confederate jasmine or a non-blooming vine like a fig ivy. Bougainvillea, more appropriately called an unruly woody shrub than a vine in my opinion, growing as a vine needs lots of sun, support, and pruning to keep blooming well.
PS. Think carefully about planting a vine, especially one with thorns, on any fence you intend of having painted ever again.