How to make player animations with CFraming?

Short Answer: You have to edit the C0 and C1 properties of the welds with a script

Long Answer: Welds have a C0 and C1 property. The C0 property determines the offset between the Part0 and Part1 of the Weld (Weld.Part0.CFrame * Weld.C0 = Weld.Part1.CFrame). The C1 property determines the offset between the Part1 and Part0 (Weld.Part1.CFrame * Weld.C1 = Weld.Part0.CFrame). That's a quick lesson on what the C0 and C1 properties of welds actually are.

Now to edit them, you need to use a script:

local Weld = INSERT_WELD_HERE

for Y = 0, 5, 0.1 do --This loop right here moves the C0 of a weld from (0, 0, 0) to (0, 5, 0) stepping by 0.1
    Weld.C0 = CFrame.new(0, Y, 0)
    wait()
end

That script will move the parts 5 studs apart in the Y direction. For more complex movements, you'll have to use angles to, like so:

local Weld = INSERT_WELD_HERE

for Y = 0, 5, 0.1 do --This loop right here moves the C0 of a weld from (0, 0, 0) to (0, 5, 0) stepping by 0.1
    Weld.C0 = CFrame.new(0, Y, 0) * CFrame.Angles(0, math.rad(Y), 0)
    wait()
end

This script will move the parts 5 studs apart but will also offset a part by an angle of 5 degrees in the Y axis of rotation. To do what you want to do, you'll need multiple loops controlling different parts of the weld components. Good luck