How do I make my curries saucier?

Ground almonds are one thing I've used in the past (usually in a yoghurt-based sauce, but not always). They give a richness without overpowering the flavour. Roughly the approach was:

• Fry onions, meat or equivalent (I usually did this with Quorn), and spices/garlic/ginger.
• Turn off and allow to cool a few minutes.
• Stir in lots of yoghurt (any natural yoghurt) and return to the gentlest heat you've got.
• Stir in ground almonds; don't be mean with them. Cook gently for a few minutes, with plenty of stirring, adjusting the texture with a little water if you like.

In a tomato-based sauce you don't need the cooling step; that's to avoid splitting the yoghurt.

Coconut flour or alternatively dried coconut milk. It's a significantly different curry because the flavour comes through, but adding either of these gives a good thickening effect (more so for the flour) that's very compatible with curries.

A sauce base using onions as I mentioned in the comments: a base sauce made from boiled, blended onions (plus garlic/ginger/tomato and a little spice) is also a good way of adding richness. This is rather time-consuming to prepare, and pungent, but freezes well.

Mango chutney is a good last-minute cheat addition, especially if you find a very sticky one and blend it first. It adds flavour and has some thickening power.

I am also an amateur, and care more about enjoying my cooking and food than about authenticity!

It's surprising when people say "I added onion" how much different variety of answers you can get, by simply asking "how much"!

Long story short, add at least four large dried (storage) onions if you are preparing a family meal and "better you pick the bigger ones", you get the idea. Also, remember to caramelise them well, if it matches the recipe, and you should not turn down adding in any fresh spring onion bunch in case you have them around. No excuses on this: onions are cheap, healthy & add good taste when cooked in the right way.

For extra thickness: I have found myself adding to my Indian-inspired dishes some yogurt. Greek yogurt tends to be thick and it will not evaporate if cooked. Ah, yes, and one more thing on this last one: NOT Greek-like yogurt, NOT Greek-alike yogurt, NOT Greek-wannabe yogurt; NOT Greek-inspired yogurt: please go and buy the real stuff! Or just don't call that other thing "yogurt", please :) Hint: it was recently found that Greek traditional yogurt is the only type in UK supermarkets which is not filled up with abnormal level of sugar.

This question comes across to me rather like: "I'm trying to make European sauce, and it's too thin".

There are hundreds of classic, that is to say, traditional dishes that have stood the test of time, from the Indian subcontinent. They come from a huge diversity of regional, cultural, and religious sources. So in that sense, there is no such thing as an Indian curry.

Maybe you are looking for something more akin to British Indian Restaurant cooking, which is much more homogeneous, and driven by a commercial need to produce an apparently wide range of dishes in as short a time as possible. Most BIR dishes are based on a single base sauce, such as the recipe here.