15:19 - And the earth We spread out, and placed therein firm mountains, and caused to grow therein all kinds of things in due proportion.
20:53 - Who has made earth for you like a bed (spread out); and has opened roads (ways and paths etc.) for you therein; and has sent down water (rain) from the sky. And We have brought forth with it various kinds of vegetation.
43:10 - Who has made for you the earth like a bed, and has made for you roads therein, in order that you may find your way.
79:30 - And after that He spread the earth.
These and other verses repeatedly mention that Allah spread the Earth like a bed - which implies that the Earth is flat. The Muslim defense comes mainly through interpreting 79:30 to mean that Earth is shaped like an ostrich egg. The justification for this is that 79:30 uses the arabic word "dahaha" which is derived from the word "duhiya" (every word in arabic is derived from its root word). They argue that duhiya means ostrich egg.
There are two big problems with this argument. Firstly duhiya does not mean ostrich egg but the place in sand where an ostrich lays its egg. Secondly even if we accept that it can somehow mean ostrich egg, the fact is that Earth is not shaped like an ostrich egg at all. Earth is roughly an oblate spheroid - which is the shape we get if we DECREASE the curvature of a sphere at its poles. Ostrich egg is roughly a prolate spheroid - which is the shape we get if we INCREASE the curvature of a sphere at its poles. A prolate spheroid never looks like an oblate spheroid no matter which angle we view it from. This is basic 3D geometry. Read this to get a basic idea on oblate and prolate spheroids.
Additionally, there is one more interesting verse that confirms the flat earth theory in the Quran.
2:144 - Verily! We have seen the turning of your (Muhammad's SAW) face towards the heaven. Surely, We shall turn you to a Qiblah (prayer direction) that shall please you, so turn your face in the direction of Al-Masjid- al-Haram (at Makkah). And wheresoever you people are, turn your faces (in prayer) in that direction. Certainly, the people who were given the Scriptures (i.e. Jews and the Christians) know well that, that (your turning towards the direction of the Ka'bah at Makkah in prayers) is the truth from their Lord. And Allah is not unaware of what they do.
The above verse asks Muslims to turn their faces in the direction of the Masjid al-Haram in Mecca, wherever they are during prayer time. Obviously since the Earth is curved, people living far away from Arabia will have their faces pointed at the outer space when they attempt to face Mecca (unless of course they are facing the ground). Again, this verse further substantiates the ignorance of the author of Quran of Earth being spherical. Ultimately, the Quran fails to explain the shape of Earth correctly no matter how you twist the verses.