Please note this answer has been heavily edited in light of a comment by quarague, who pointed out an error. It ended up being incomplete as a result of that, but maybe it's helpful as a starting point for someone else.
Your 4D planet has two equators. I'm assuming the sky is similar to ours in that it has a number of fixed stars, although of course the sky appears to an observer on the ground to be a three dimensional surface instead of a 2D one.
To specify a point on your planet's surface we need three coordinates. I originally thought these would consist of two latitudes and one longitude, but quarague pointed out that it's actually one latitude and two longitudes, as I'll explain.
We can define the latitude as the angular distance from one of the two equators, just as we do on Earth. The reason there is only one latitude instead of two is that they determine each other - if you're 10 degrees away from one equator then you're 90-10 = 80 degrees away from the other. (This means that each equator acts like the "pole" for the other, so if you're 90 degrees from one equator then you're on the other equator. This explains the lack of poles.)
Now consider one of the fixed stars. Think of its position as a vector, pointing out from your planet's centre to the star's position, so that it passes through the surface at a point where the star is directly overhead. As your planet rotates, the position of this point will change, since we fixed our coordinate system to the planet's surface.
However, I believe that the latitude of the point will not change. This is because rotations preserve angles, and the rotation of your planet also preserves the position of each equator. So the star's latitude stays fixed over time, just like it would on Earth.
The first step in finding your position on your world would be surprisingly similar to how it is on Earth. You simply take out your 4D equivalent of a sextant (whatever that is exactly) and measure the exact position of a star in the sky, or more likely several stars. From this you can determine your latitude.
I'm skipping over a lot of details here of course, mostly because I can't easily visualise them, but I suppose the process would be similar in principle to how it is on Earth: you measure the distance of the star from the horizon and calculate your latitude from that. Maybe you need a compass as well, which will make things tricky given the absence of poles (and also of electromagnetism as we understand it). But in principle it should be possible to get your orientation from star positions as well, if needed.
Just knowing your latitude is probably much less helpful on your world than it is on Earth, because there are still two dimensions in which you don't know your position. These are the two longitudes.
I do not know how those would be calculated, however. My initial guess was as follows: your world has two different day lengths, which correspond to its rate of rotation around each of its equators. (The two day lengths are necessarily different, otherwise there would be an infinite set of equators instead of two.) I thought that maybe the two longitudes would correspond to the time of day according to each of the two types of day. But I don't think that can be right, because in the end the data you get from a chronometer is only one number, whereas we need two independent numbers in addition to latitude in order to specify a position.
So currently this answer is incomplete - I will have to think more about what the two longitude-like coordinates are and how one might go about measuring their value.