If I were you I would prune after the berries become dormant. You will probably want to thin them out so that you have no more that 5 or 6 canes, keeping the best one that did not fruit. Cut them back to 3 or 4 feet long and tie them to the trellis.

Here is a picture of one of the plants. I am planning on building a T type trellis

The bed I have these in is around 17 feet long and 3 feet wide. Originally I had planted four plants in this. The 2 middle ones didnt make it. Is four an ok number for a bed this size or should I just do three?

Here is the other plant

Four plants is fine for 17 linear feet of bed. If you want to replace the middle two plants, try maneuvering some of your cane tips to the middle of the bed and see if they will take root overwinter. Just nose them into the soil slightly.

Otherwise it is a fine time to prune the canes, just prune them to the same height as your trellis and tie them up. Each cane could potentially produce a pound or more of berries, plan on what to do with all that or else prune out more canes.

I agree with larry. But if I were building the trellis, I would sink concrete-anchored treated 4X4s 8 feet long in each end of the bed. Dig your holes 2 feet deep and connect the posts with five 12 guage wire strands. This gives you a six foot high trellis. Every six feet drive in a metal fence post to give the wires additional support. I would not use a T trellis for blackberries. With the one I described you can run your canes at various levels. To replace the middle dead plants use the ground layering technique by burying a portion of one of the canes until it roots, then cut it free from its mother.

So basically take the canes, stand them straight up and tie them to the trellis. Cut them off at the trellis height and tie or weave any lateral branches onto the trellis? What about lateral branches that are above the trellis height? These will be fruiting won't they?

Or do I just weave the whole thing on the trellis?

My blackberry trellis is built with 10 foot electrical conduit poles, sunk 4 feet. No cement, are 24 feet apart and bend inwards when you use wire tighteners, but need no other support, and is super cheap. Poles are about 5 bucks each.
You can buy 2 grades, the higher grade is more expensive and super thick, it will not bend with hundreds of pounds of pressure. I use the cheap grade myself. I don't care that they bend slightly, they are not going anywhere! And will never rot.
Most laterals are cut to 18 to 24 inches, but if I can fit them somewhere I leave them slightly longer. It is said if you trim the vines and laterals the berries will be bigger. Too much length produces smaller berries, but I myself wish to see for myself, so some are long, and some are short on different plants.

Black Satin laterals generally go off at right-ish angles, so by definition they would not extend above the trellis.

The laterals will be fruiting, along with the main canes. Bundling 3 or 4 together is fine, small numbers of laterals do not have to be spaced out. Again, consider what you will do with a large quantity of berries before keeping a large number of linear feet of laterals.

Take care when standing them straight up; they have grown along the ground and may weaken or break at the base if forced too upright. The diameter of your canes looks fairly small and they may be very flexible.

I guess what I was asking with the laterals, is that there are bound to be laterals above the height of the trellis since the canes are so long. I just cut the main cane off at the trellis height and lose the laterals above there? Perhaps that concentrates the plant energy into making larger and mrore berries on the canes that are left?

Yes they say larger and more berries if pruned, you can weave the vines around two lines also. Just fit the laterals where you can. Many of my vines overlap.

Ok I think my last question regarding blackberries....for now.

Should I string them up on the trellis now or wait until spring?

I would do it now, but I don't believe it matters. Typically, the canes are tied to the trellis after they are pruned in late winter.

String them up now--unless you will need to mulch-protect them overwinter for survival (many zone 5 and 6 growers cover their canes overwinter, but you are in 7). Berry size does not taper off on healthy watered plants until the cane diameter gets very thin near the cane ends--and that part is usually pruned off.

Some gardeners leave trailing type protocanes on the ground until fruited canes have been cut down, that eliminates the possibility of pruning off a first-year cane by mistake. Is there any other activity around your berry beds--soccer balls kicked, dogs, cars?

If there are laterals formed above trellis height, you can either prune them fairly short or if the laterals form a T at the end of the main cane, prune one lateral off entirely and treat the whole thing as one long cane.