I am a total beginner to the trumpet. (After 50+ years of clarinet playing, I just took the trumpet out of the case!). I see that C and G are open notes--how do you know which you are playing? (Is it about how hard you blow?) I also see that both E and A are the first two valves. How do you know which note is E and which is A? Also, how do you tongue on a trumpet? It doesn't seem the same as on a clarinet. It seems I have to blow pretty hard, but I getting some clear notes.
A very beginning trumpeter.
Welcome to the "dark side". LOL. You're finding out just how physically demanding trumpet can be and that muscles seriously have to be trained and worked on day in and day out for you to progress.
I will answer your questions:
1 - Notes. The partials you are finding are indeed there. In fact, you're merely skimming the surface right now. You found C and G, but there is a 4th space E that can be open as well OR you can play it 1 & 2 (depends on how in tune you are there). Your real question seems to be how to work on being in command of the various notes based on the fact that there are no "fingerings" to help. First, you have to listen. You're in the same key as clarinet and you know a basic note sound. However, what I might suggest is that you use a simple tuner. Most beginners start on that second line G as their first note they play. They OWN that note and the notes immediately around it. Are you working out of a book at all? I will assume so. Essential Elements does a nice job getting you started. By page 10 you should be playing some 5-6 note songs. The key to your answer lies in long tones. This does two things. One, it solidifies the note in your ear and in the face muscles. By long tones, I mean holding that note with a steady stream of air and for as long as you can and still get a good tone. Do this with every note you learn. Secondly, long tones works on air production. Air is invaluable in all wind instruments, but when you get that kind of back pressure from a brass instrument it becomes even more so. Big, full, RELAXED breaths and control when you are producing notes. Avoid the tone wavering as much as possible. Keep the stream steady.
Another HUGE help here is JUST mouthpiece buzzing (no horn) and match pitches. I buzz with the radio or whatever and really train my ear and face muscles to make the sounds I want.
2 - I hate to say this, but the tongue process is not cut and dry. When you begin trumpet playing, instructors try and get you to thing "TA" or "DA". If you say those without a horn, that is what the feeling should be with a mouthpiece on your lips as you produce a tone. I have had instructor teach the breathing and release of air like this: say HOW on the inhale (sucking in air) and TO on the exhale with no stopping in the middle. Think circular. The best way I have found to work on tonguing is when you do your long tones like above, INTERRUPT the air with the tongue with a "TA" or "DA" approach. I like DA better because the tongue doesn't sound as harsh or staccato. It seems to come out smoother. It's up to you and you will use both eventually depending on what you're playing. Think of your air stream like water coming out of a hose. Then think about your hand passing through the stream of water and interrupting the air. The flow doesn't stop, but the TA/DA gets in the way.
YES, you do have to blow hard it's really about a relaxed inhale and exhale with the control happening once the air is released. Keep the shoulders and neck relaxed. If you don't, the sound will come out tense and small. Keep everything open and as full as possible. Again, the mouthpiece only work will help. Involve you clarinet or tuner that makes sounds. Get a note going and match that pitch using the mouthpiece only. Get as FAT and full of a buzz as you can and match that pitch. There resistance is so limited in mouthpiece only work that if you can get a big sound on just that your tone will be a ton better AND the back pressure of the horn will actually make the production of the notes easier the more you do it.
I hope this helps. If you need any further ideas, I am happy to be a part of your journey. I am honored you reached out.