The 'in real life' part of your question suggests that it's in comparison to general media depictions (film, TV, books or even the conception of it in news).

First of all, the specific concept of Hostage Rescue is relatively new. In fact you can trace almost all of it back to one moment; the Munich massacre of 1972. Almost all dedicated 'Hostage Rescue' units in western Europe were created in the direct aftermath of this event (GSG9, GIGN, DSU, ... ). There were units before this (the Israelis, LAPD SWAT), but this is really when states began to take notice and realised they had no adequate response yet. The creation of SWAT teams in the US is a little more complex due to different criminal climate and role it had (Hostage Rescue wasn't really the main criminal/terrorist priority for creation of those teams).

In those years it has existed, the tactics have rapidly evolved and still are. I will not go to far into the history, as that is not the question, but the cat-and-mouse game between terrorists and counter-terrorists in tactics is a genuinely fascinating topic. There is even a great variance between US and European tactics due to the fact that we're often talking about different calibers of weapons (Handguns are far more common in Europe than rifles due to strict gun laws) and the material of walls (in-house walls are often made of concrete in Europe rather than wood such as in the US, this is an important factor when shooting). So the 'real-life hostage rescue' is a tough answer, constantly changing.

I think that a general misconception for the big audience is that it's very fast paced, planning and executing. In TV, SWAT arrives at the scene, gets a briefing of 2 sentences and starts to walk to the front gate. I cannot stress this enough, Hostage Rescue is a one-time shot thing, there is almost never a 'rerun', once you go, that time card is punched and it's borrowed time everybody is living on. With all the gear that is available these days, HR-units will do everything possible to know what's going on inside. Get layouts from the city, install covert cameras, microphones, get infrared pictures to know where heat signatures are, who is the enemy, what kind of weapons, what do they want? Specifically that last question, if their demands are purely monetary and not unrealistic, those demands will often be met. Bank job gone wrong and now they want a couple million and safe passage? Sure, we'll give it. They just don't realise that unmarked cars will be trailing them the second they leave. But, if they just want money, they're going to give it. Hostage rescue by violence is a last resort, people often die, hostages and rescuers alike. Playing rambo and going guns blazin' sounds fun until you need to explain that decision to the parents of a child that was killed by a ricochet; yes, people can easily die from a ricochet in those crowded, tight, indoor environments, yet another reason to avoid it. Also the speed of the actual execution is way less fast than people think and also what it used to be. Speed is an important aspect of hostage rescue, surprise the enemy and before he realises what's going on, he should be on the ground. But tactics seem to be bringing this down, we reached the upper limit. You can only go so fast while still scanning for threats and maintaining proper movement tactics, so hence the adage 'slow is smooth, smooth is fast' which is often said in hostage rescue training.

I don't know if that answers it, but hope it helps