As mentioned in the comments, the additional content immediately appears at the places on the map where it can be accessed. However, it is useful to know where to find them if already have explored a lot and don't want to backtrack.
Apart from the minor improvements (e.g. charms), the major part of the Grimm Troupe update is available after 'summoning the troupe' at a small cave accessible from the large cliff on the west of the Howling Cliffs. After that that, the Grimm Troupe appears in Dirtmouth.
The Hidden Dreams content doesn't really have a quest like the Grimm Troupe, but a noticeable piece of content is the Dreamgate (unlocked after gathering enough Essence) and some two bosses in dreams that are hidden:
"Grey prince Zote". Found in Bretta's house. Unlocked after both saving Bretta and defeating Zote in the colosseum. This of course requires you to not let Zote die when you encounter him, so this is the only part on which you could miss out in your current play-through.
"White defender". Found in a hidden room near the Dung Defender. Unlocked after defeating the Dung Defender and all three Dreamers.