For a terrestrial planet to have several moons, they would either have to be very small or in very different orbital distances. Both are the case for Mars' moons Phobos and Deimos.
The concept of a Hill sphere provides the answer. The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. The Earth's Hill Sphere has a radius of 1.5 million km. However, long-term stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. For Earth, this limits the orbital distance of a stable moon to between 500,000 and 750,000 km. Let's go with 500,000 km to be safe. Our moon (Luna) orbits at 362,000-405,000 km.
Each moon also has a Hill sphere. Another stable moon would have to lie outside the reach of this. Luna has a Hill Sphere with a radius of about 60,000 km. Hence, it is feasible to have several Luna-sized moons in orbits at least 60,000 km apart. Due to tidal effects and other perbutations like the pressure of the solar wind, 100,000 km is probably a more realistic figure, and even so, the orbits are unlikely to be stable over the planet's lifetime - but could be stable for millions of years. It is hence possible to have one moon outside Luna's orbit and up to three inside. With a slightly different configuration, we might have up to 6 moons in resonant orbits, as I show below.
Hence, it is (barely) possible for an Earth-sized planet to have up to 5 Luna-sized moons in somewhat stable orbits. The most likely solutions would put the moons into orbital resonance, like the Jovian moons Ganymede, Europa and Io, with a 1:2:4 resonance.
Let's put the innermost moon at 120,000 km. The next moon, in 2:1 resonance, would then orbit at 190,000 km. It is just possible to have the next moon at 3:2 resonance with this (and 3:1 with the innermost moon) at 250,000 km. Let's make this moon a bit smaller, just in case. 4:1 resonance with the innermost moon is not possible, as it would put the moon too close to its inside neighbor. 9:2 is possible; a 3:2 resonance with the third moon. This puts the fourth moon at ca. 330,000 km. The next moon could be a 6:1 resonance with the innermost, at 400,000 km. A sixth moon at 9:1 might just be possible at 520,000 km. The innermost moon would then have an orbit of ca. 12.5 days, and with the rest orbiting in 25, 37.5, 56.25, 75, and 112.5 days.
This would however be a very extreme situation, and you only ask for three or four moons. Let's go with 4 moons at place them at orbital resonances of 1:1, 2:1, 4:1, and 8:1 - each moon having twice the orbital period of the one inside. Again placing the innermost at 120,000 km with an orbital period of 12.5 days, we get distances for the others at 190,000, 300,000 and 480,000 km, with orbital periods of 25, 50, and 100 days.
We assume that these all orbit in the same plane and in very nearly circular orbits. Tides will be much stronger than on Earth. the innermost moon will exert almost 80% more tidal force than Luna on Earth, the second 40% more, the third 30% more, and the outermost 10% less. When all moons align, their combines tital forces wiill be 5.4 times that of Luna on Earth, for very powerful tides indeed. This actually happens every 100 days because of the orbital resonance! Earthquakes are probably more likely when this happens. To this we can add solar tides, which on Earth account for one-third of total tidal forces. When the four moons align with the sun, tides will be extra high.