I've been playing support recently, and I find myself making the calls. Mostly I say to go for objectives, such as towers, dragon, or baron, but many times my team and I get caught in a bad situation.
When and where do we go in different situations? Some examples could be helpful. Thanks in advanced. :D
It IS very situational but I'll try and give you some more common situations for each objective:
Dragon: There's a lot of situations you can go for dragon.
Towers: Some teams are just really good at taking towers making it safe to do so (i.e you have a Cait on your team). Other teams, say with Twitch, are not so good at taking towers. You really need to judge your team comp for this one so it's hard to even give you situations. If you have a split push/poke style comp (see Cait example) you'll want to constantly be pushing towers and then disengaging. If you have a team fight oriented team (such as Twitch) the safest way to take towers is to first team fight and then if you won to take towers. The most important thing is to keep track of the enemy, make sure you have wards, don't over extend without wards, don't overstay and make sure you always have an out if you need one. If you're taking a tower because you killed someone on the enemy team, watch their death timer. Try and push with minion waves to make it easier.
Baron a.k.a throw pit: Honestly, the best situation to do this in solo queue is only if you aced the enemy team. If you're super ahead, it can be a good catalyst to push the game to the end. You really have to be careful with this though. If it's risky at all to do it I would say stray away from it. Unless it's a last ditch effort because you're about to lose, or you're so far ahead you're acing the enemy, it's best to stray away from it. There are situations to take it though, such as:
There is not a standard set of shot calling rules. You have to make the best decision based on the facts. Pay attention to the minimap, do you know where all the enemy champions are or just were? Do you have good vision around the objective you want to call for? Are you tracking what summoners your teammates and enemies have used/not used? Are you ahead, behind, even in gold/items? You have to be aware of all of these things, and then some, and try to make the best educated guesses/ shot calls that can help your team. A lot of it comes with practice. For example, the enemy jungler ganks top, you can push the wave and your jungler is in your side jungle, PROBABLY a safe time for dragon if it is up. That is a common strategy, but it isn't set in stone or 100%, you have to consider all the facts.
Start by doing this. After you guys WIN a teamfight, if you have a healthy adc still, try to push a tower, but if you guys barely won and have to limp off, throw down some deep wards in strategic points around the objective you want to go for in the next 3 minutes. If you start paying attention to the factors that you can keep track of, and then thinking ahead to 1-3 minutes from now, you can start to make better calls.
Important thing about shotcalling is to understand that if your calls aren't followed, then it doesn't matter how good they are.
Something simple like pinging Dragon after winning a fight in the bot jungle, most people will listen to. It's a simple, straightforward call that almost everyone sees the value in.
Meanwhile, spamming "we need to group guys, we need to group, we need to group, plz group" is generally pretty pointless. You're not asking people to centralize around a specific objective at a specific time - almost noone's going to listen to a call like that if there's farm to be had in a side lane, or a buff to be taken, or whatever. Maybe grouping is the right call, but it's not specific enough to mean very much to most players.
You also need to respect your teammates' champion choices when you make your calls. If you have a full damage Master Yi with teleport, respect that he probably wants to splitpush, not dance in the Baron pit for five minutes with the rest of your team. And respect that he's probably right. Proper calls are generally pretty situational, because each game brings different factors.
Main Objectives:
Dragon
When to take dragon?
When do I prioritize dragon over anything else?
What champions are good at taking dragons?
Champions such as 
are good because they either have good life steal so they can tank the dragon and still be healthy if a team fight breaks out, or they have very low steal chance from the enemy jungler. Also champions that deal damage bases on % maximum health can do a lot of damage quickly to the dragon since it has a lot of health.
Baron
When do I take baron?
Numbers 1,3,5,6 all apply here. The only thing to watch out when taking Baron is if you are pretty even. If the enemy team starts attacking you just peel off of baron attack them. Try to move past them so that the baron loses aggro on to you and starts attacking them. Baron fights are typically where the biggest throws in any game happen, whether its from a missed smite or just taking too much damage from baron.
What champs are good at taking barons? The same champions apply to the baron and dragon.
Towers & Inhibitors
When to take towers?
I hope this helped. I wish you the best of luck on the fields of justice.
If you try to shotcall in Gold elo, good luck, maybe like 60% of the time I can do it, but the rest of the time no on listens.
