When you push d4 early on, the general plan is to protect the d4-square and e4-pawn, while developing quickly. With your king out of the centre things tend to become easier, and you can focus on more long-term plans. Meanwhile, if Black clamps down on the d4-square with ...e5, then they have also weakened their d5-square. Here the plan is to capitalize on the d5-square (not necessarily with an immediate Nd5), and to play on the flanks (for example, with a3, Rb1, b4).
I'll outline some theory for the lines you mentioned in your comment. At the end of my answer I'll give what I think is a better way to play the e4+c4 system.
1.e4 c5 2.c4 Nc6 3.Nf3 e6 4.d4 (delaying d4 with 4.Nc3 and 5.Be2 is also possible) 4...cxd4 5.Nxd4 Nf6. After 6.Nc3 Bb4, your e4-pawn is under attack. It is best to defend it with your light-squared bishop, but right now Bd3 loses to ...Nxd4. So you should play 7.Nxc6, and now there are two main responses:
7...bxc6 8.Bd3. Now Black may strike in the centre with ...e5 or ...d5 (before or after castling). For example, 8...e5 (8...d5 is met with 9.exd5 exd5 10.0-0) 9.0-0 0-0 doesn't give White any advantage, but the position is playable. A possible continuation is 10.Be3 Bxc3 (10...d6 could be met with 11.Qc1 followed by a3, since ...Bxc3 no longer gives you doubled pawns) 11.bxc3 d6 12.c5!?.
7...dxc6 8.Qxd8+ Kxd8 9.e5! Ne4 (or 9...Nd7 10.Bf4, followed soon by 0-0-0) 10.a3 Bxc3+ 11.bxc3 may give White a pull. He has the two bishops, while Black's minor pieces aren't that good (for different reasons). Note that 11...Nxc3?! should be met with 12.a4, when White may meet ...b6 with Be3 and a5. He has enough compensation for the pawn to claim an edge.
1.e4 c5 2.c4 d6 3.Nc3 Nc6 4.Nf3 g6 (4...e5 looks good for Black). Here White should play 5.d4 cxd4 (or 5...Bg4 6.d5 Nd4 7.Be2) 6.Nxd4 Bg7 7.Be3, but now this transposes to a line in the accelerated dragon. The theory here is well developed, and I'm not sure if this is what you're interested in, considering with 2.c4 I assume you're trying to avoid Open Sicilian lines.
1.e4 c5 2.c4 Nc6 3.Nf3 e5 4.Nc3 d6. Here I don't like the immediate 5.Nd5, and instead 5.d3 looks better (followed by Be2, 0-0, etc). The problem though is that Black can push ...f5, whereas you can't push f4 since the knight is already committed to f3. This gives Black at least equality, and while the line is playable, it would be better if your knight was on e2. After castling you could try playing on the queenside with a3, Rb1, b4 (and Nd5 if the position calls for it), but Black's kingside play looks easier.
In my opinion, due to the possibility of Black playing ...e5, I think it's best not to play Nf3. Instead, a setup with Nc3, g3, Bg2, Nge2 looks stronger. Then, you may continue developing with 0-0, d3, Be3, Qd2, f4, etc. The d4-square will remain a hole for now, but in general your setup is pretty harmonious. In addition, you can play it against a variety of different systems Black has.
A good introduction for this opening on YouTube is a video on the Botvinnik-English system by the Melbourne Chess Club channel.