Use welding.

https://developer.roblox.com/api-reference/class/Weld you would want to change the property of part1 to be the part and part0 to be the player and use C0 to move it around

    local Weld = Instance.new("Weld")
    Weld.Parent = Head
    Weld.Part0 = Head
    Weld.Part1 = Hair
    Weld.C0 = (CFrame.new(0, 0.9, 0.3)) * CFrame.Angles(math.rad(0), (0), 0)

This one is for hair

I dunno cuz I a "smart"

Weld

As mentioned in a couple answers, welding is often used to attach objects together. You would weld the model together itself, then weld a part from that model to the character.

I want to mention something here. If there are many parts in the model, I would not suggest welding them but rather making them a mesh or union. I made scripts for a clan and encountered lag issues due to too many moving parts.

Loop

By loop, I mean like using RunService to continuously set the PrimaryPart CFrame of the Model. This would be impractical but could work depending on what you are trying to achieve.

Animation

I would recommend animations for attaching things to players. It may be tricky to do depending on the situation, but it comes in handy in the long run.

It makes transitions smoother, is less laggy since it is client-based, and it is easier to use. This would require the model to be a mesh or even a combination of welding.

Explore other methods and do what suits for you! Good luck!