How can I get started in molecular biology?
First develop a background of basic highschool chemistry, basic biochemistry and basic genetics. 

What is molecular biology: Molecular biology has 2 definitions. A broader definition is molecular basis of life. That is indistinguishable from biochemistry. The second definition is how does genetic information flows through 
 molecular mechanism. The secod one is a more specific definition of molecular biology and how it differs from biochemistry. 

Its good to develop some background in biochemistry and genetics because concepts of molecular biology comes from biochemistry and genetics. 

A quick start through biochemistry: 


Lippincott's illustrated review on biochemistry.   
Harpers's illustrated review on biochemistry 
Organic chemistry by Solomons and Fryhle (especially stereochemistry portion). 


then go through gradually more detailed book, such as biochemistry by Lubert Stryer. 

Parallelly go through Genetics book such as 


Principle of genetics by Hartl and Jones 
Gene IX by Benjamin Lewin
Principles of genetics by Snustad et al. 
iGenetics by peter J. Russell
Concept of genetics by Benjamin pearce 
Genomes 3 by T A Brown 
Principles of gene manipulation and genomics by RM Twyman and Sandy B Primrose. 


Each book has a different perspective. it will help a clearer picture of different concepts. 

Some basic molecular biology books: 


Molecular bioloy- principle of Genome function: by Nancy Craig et al. 
Molecular biology by RF Weaver. 
Fundamental molecular biology - Lizabeth Allison 
Princiles of molecular biology by Barton and Tropp. 


For a more cellular approach and bigger picture see cell biology based molecular biology books viz. 


Cell biology by Pollard, Earnshaw et al. 
Cell biology by Gerald Karp 
Lewins' CELL by Plopper et al.  
The Cell- a molecular approach- by Geoffrey M. Cooper.