If you have the Synthesis Scanner out and the target is in the same 'room' or one over, Simaris will say you've found it and it will appear on the mini-map. It will be the glowing purple target (like the glow from Grineer Guardsmen).
If it all seems a bit confusing, you can talk to Simaris again and he'll stick you through a short tutorial.
A word of warning, I highly recommend doing Synthesis missions solo though (The New Strange excepted) as people will only get the Simaris blurb at the mission start if they have a Synthesis scanner equipped and may end up attacking it. You also have the arsehats who intentionally kill it or won't give you the time to locate and scan the target.
On the plus side, if you have people who are also properly hunting targets, you only need to be near by them and you both get the standing gain up to the daily cap.
Once you've completed The New Strange, you have a choice of targets you can hunt for (console to the left of Simaris' room) and he'll give you a daily target. I highly recommend the wiki to look up the base level so you can find the right missions for the target to spawn in.
You can also scan any enemy for Simaris standing with the Synthesis scanner instead of affinity with the codex scanner, although I recommend getting the infinite scans widget first (synthesis scanners are 10 times more expensive than codex scanners at 5,000 for 25 instead of 500 for 25).
Synthesis targets only spawn if A) someone has a Synthesis Scanner equipped and B) their target (either Simaris daily or chosen from the console) is in the mission they're currently running. As mentioned earlier, if you also have a Synthesis Scanner equipped you'll get the same message from Simaris and you can piggyback on their standing gain.
If you don't have the scanner equipped, you won't get the message and may miss it entirely except for this really tough glowing purple target. If you don't have the scanner out when the target is found, you'll miss the "it's here" message and mistake it as a boss (I accidentally did this last night as I mistook a broodmother synthesis target for a juggernaut on an infested mission. In my defence, I've never seen a juggernaut as it's either dead by the time I reach the rest of the team or it moves on).