There is a couple different ways to determine if a bond is ionic or covalent. By definition, an ionic bond is between a metal and a nonmetal, and a covalent bond is between 2 nonmetals. So you usually just look at the periodic table and determine whether your compound is made of a metal/nonmetal or is just 2 nonmetals. The exception is a compound made with ammonium (NH4+) Since ammonium is an ion, it forms ionic compounds. If the compound begins with H, it's an acid.
You can use determine the difference in electronegativty. This is a value that rates how attracted an electron is to a particular atom. This value is often stated in a chart or on the periodic table. Find both elements in the bond, and find the electronegativity values. For example, Na is 0.9 and Cl is 3.0 Then subtract to find the difference (3.0-0.9 = 2.1) Using this method, you can determine the value of each bond.
If the difference is between 0.0-0.3: The bond is nonpolar covalent
If the difference is between 0.4-1.7 (Some books say 1.9): The bond is polar covalent
If the difference is greater than 1.7 (or above 2.0 in some books): The bond is ionic.
As for shapes, you need to first draw a lewis dot structure (LDS) for the molecule. Based on the LDS, you can determine the shape. If the LDS has 4 surrounding atoms/4 single bonds and no lone dots on the central atom, the shape is tetrahedral. If it has 3 single bonds and one pair of lone dots, the shape is trigonal pyramidal. If it has 2 single bonds and 2 lone dot pairs, it's bent (bent also goes for 1 single, 1 double, and 1 lone dot pair).
If the LDS has 3 single bonds (or 2 single/1 double) and NO lone dot pairs, it's trigonal planar.
And if the LDS has 2 double bonds and NO lone dot pairs, or is just 2 atoms, the shape is linear.