First of all I created a cylinder by going Create > Polygon Primitive > Cylinder

Initial cylinder

In the input section I changed the Subdivision Axis to 24. This created more areas for me to manipulate the cylinder. 

Cylinder with subdivisions

In face mode, I used the paint selection tool to select all the faces. 

Then using the extrude tool I moved it upwards and then brought everything in from the centre. 

Next I repeated the process using the shortcut 'G' to extrude, creating another ring from the centre and moving this up slightly as before. 

I repeated this stage again, creating an even smaller ring. 

Next I added a sphere, making sure it had 24 subdivisions - the same as the rest of the UFO.

I went into side view by holding space bar > Maya > right view. Then while in face mode I selected half the sphere and deleted it. 

I deleted the faces of the circle where I wanted to place the semi - circle by using the paint select tool, highlighting the faces and hitting backspace. In the top view I positioned the semi-sphere over this. 

I then made it bigger to fit the area using the scale tool. 

Back in perspective view, I selected both shapes together and then went Mesh > Combine to combine the two shapes. 

As you can see even though the objects are combined, the vertices are not. I went to vertex mode > merge vertex tool. I then clicked on the vertices' points on the sphere and alligned them with those on the rest of the ship, therefore merging them together. 

Pre-merged vertices 

Original softened look

To get the more distinct look, I went into edge mode and double clicked on the connecting edge to select the entire line. I then went Normals > Harden Edge. 

Entire edge selected

Hardened edge

Using the paint selection tool I selected the upper faces (the sphere and circle around it). I then used the move tool to move these upwards more

Next I highlighted the faces of the outer circle and using the extrude tool, moved it downwards. 

To begin on the bottom of the craft, I selected all faces again and then using the move tool, moved it upwards to make the base of the craft thinner.

Thinner base

With the faces still selected, I used the extrude tool and then using the move tool, moved it downwards. 

Then using the scale tool, I moved the base inwards, as shown below.

Next I went to Mesh Tools > Insert Edge loop tool and added an edge in the centre. 

Added edge loop

Highlighting the bottom faces and then using the extrude tool, I moved the bottom face upwards forming an indentation to wear a light beam could come out of.

Continuing on the bottom I highlighted every other face, extruded and then moved these inwards. Selecting the edges where the faces connect to the beam section, I used harden edge on them. 

This is the final UFO model. The next stage will be designing it in photoshop.