If you go to openstreetmap.org and click on edit, that will get you the iD editor.
In it, you look for the road you’re interested in. If you’re lucky, there will be a node (point) right where you want to change the speed limit. It may or may not represent a split in the segment (it could be something else), if it’s not you need to create a split there (see below),
If there isn’t a point where you want it, you can add it by double-clicking at the relevant place on the road.
To split a segment at a point, right-click on the point and you should get a mini-menu pop up with 4 items, you want the scissors.
Once you’ve split the segment, click on it to highlight it and check the highlighted bit is correct. Then you can set the speed limit in the left pane.
If you’re using potlach (deprecated) then you’ll have to wait for somebody else to answer.
Remember, the undo button at the top of the window is your friend. 
