I like the manual guns as well so I can feel how the zerk is taking grease. Here are a few things that might help for general greasing tips for a very new person.
Clean off the zerk before you grease so you don't force dirt into the bearing.
Make sure the end of the grease gun is clean, push a little bit of grease out and wipe it off if the end looks dirty. Again, keeping dirt out of the bearing.
Some Moly greases are not happy with high speed bearings, they can cause separation of the moly from the grease base and gum things up. If you are greasing bearings that go fast, say over 300 RPM, make sure your grease is happy with bearings. It might say something like OK for wheel bearings or something like that.
Different types of grease don't always play well together, for example lithium and polyurea are not always compatible. Some are though so just read your label to know what kind of grease you are using and stick with it. You can change in the future, just make sure they are compatible. If not then you would grease until the new grease comes out clean, flushing out the old grease.
Grease comes in different thicknesses for different applications, read your manual to make sure you don't have a special case but 99% of the time you just need the standard viscosity which is NLGI 2
If the zerk has something near it and is a pain to fit the tip over, they do make pointed tips and needle tips that just fit in the end of the zerk and push the bearing down so you can grease without having to put the head of the gun over the entire zerk.
There are in general 3 ways that a person greases something with a grease gun. There are lots of exceptions but unless your manual says something different these will give you a great start.
1. Joint that is sealed with a rubber or plastic boot, an example is a steering arm on a car or truck. When you grease, the grease will start to expand the boot. In this case grease until you see the boot start to grow. You can break the boot so you are just looking for a small expansion, once you see that stop and you are done.
2. This one and the next one are similar, the difference is when you stop. Grease until you see old grease start to come out of the pin, joint, bearing, etc. This is the method on most things.
3. This is like the second but keep greasing until you see clean grease come out. You are totally flushing out the pin, joint, bearing, etc. You could do this with everything except it makes more of a mess because of all the excess grease. Sometimes though you do want to totally flush things out. An example is the bearings on my equipment trailer, there is a zerk in the hub which will grease both bearings. The manual states to keep greasing until it is clean coming out the end of the axle. Normally these situations are done for things that are not greased a lot. Things you grease every 8 hours for example get number 2 while a once a year or once a month are more likely to get number 3. Your manual should tell you if you need number 3.