GET your REST data and store in a PowerShell object:

$Post = Invoke-RestMethod -Uri "<http://jsonplaceholder.typicode.com/posts/1>"

Modify your data:

$Post.title = "New Title"

PUT the REST data back

$Json = $Post | ConvertTo-Json
Invoke-RestMethod -Method Put -Uri "<http://jsonplaceholder.typicode.com/posts/1>" -Body $Json -ContentType 'application/json'