It's fairly easy. Just bend the vines over in the direction you want them to go, and push a stick in the ground to keep it from flopping back. If it's too radical to do at once, do it in stages.

Looks like Echeveria Perle von Nurnberg (need front view). They will grow tall trunks; definitely change potting mix, it is too wet. Only way to 'change' it is to behead it - cut off top rosette, let callus and pot into grittier mix. You could leave original stalk potted as it likely will grow few babies too. The new plant will grow similar, but it will be a while before you need to do it again. Here is one that was cut off about week - 10 days ago, new branches are starting to grow - sorry it's such a blurry photo... Edit: Jeff just posted...he knows better :)

Paul and Christina I like your thinking! :-) Paul, the common/shared balcony does get some weather but not with the same force or as much rain as mine. I've never noticed a power outlet on the shared balcony, but I wouldn't use it anyway because we have a lot of people here that have absolutely no idea of safety. We have another balcony directly above ours the same size as ours, so there is better shelter from the elements. My balcony also has a small balcony above, the same size as mine. Oh my goodness! I have the same sort of shelving in my room, of the first image from your link lol. I bought expensive ones so they can hold more weight than I could ever manage. I did put the small one outside for a short while but it started developing surface rust pretty quickly. But I've noticed recently much cheaper ones of the same design. What type of store is the BBS? I wouldn't like to tie or even chain anything from the balcony fence above and we have asked permission to get hooks for hanging plants, I even offered to pay to get them to get professionally done, a firm no :-( By the way, I have often used zip ties with far greater success than even strong wire, and cheap enough to replace often if needed. Christina, I love the lockable wheels thought! Then I could even take them from the shared balcony to mine and vice versa. And even inside if needed. Just had a thought! We have a walkway across to the next building/wing of the complex, that I've noticed gets full sun for quite a few hours in the middle of the day. I also have a few trusted friends on my floor who's balconys face north so should get the hottest sun for many hours. So...... cheap shelving with wheels, maybe 2 if needed. Roll the plants all over the place to get the best conditions available for any season lol. Equals - I may be able to keep and add to my Succulents after all!!! Woooo hooooooo :-D Also very spoilt plants lol. Also equals a very long post. Sorry guys. But thank you so much!!!!

That is really huge pot for such small plants. I don't know what you have them potted in, but too much of mix - if it doesn't drain really fast - could create a problem sooner or later. And plants seem to be lost in all that extra space. If your plants lean, that is definite sign of insufficient light and should be corrected. Otherwise, they will grow weak and spindly looking, and probably not as well colored as they should be. Even plants that trail or grow longer stems naturally should have sturdy stems.