If you want to create an IPTG-inducible system in E coli, you actually have two choices: 1) you can have the lacIq repressor module encoded within the vector itself, as is the case with the commonly-used pQE-80L backbone (https://www.addgene.org/vector-database/3883/). In such a case, you put your gene of interest in front of the T5 promoter and could express it in an E. Coli strain like DH5-alphas (which are typically used for MiniPreps, rather than expression). 2) Your other choice is to use an expression-optimized backbone, such as pRSET and its variants (https://www.thermofisher.com/order/catalog/product/V35120) and place your gene of interest in front of the T7 promoter. You then transform this into the popular E. coli strain of BL21(DE3), where the λDE3 prophage was inserted in the chromosome of BL21 and contains the T7 RNAP gene under the lacUV5 promoter. This strain and its derivatives is by far the most common for protein expression because the strain itself has the lac operon, thus its not needed in your vector. In both cases above, you may wish to add some dextrose solution to the culture as it grows to inhibit protein production until you reach the proper optical density for protein production (between 0.6-1.0) before then adding your IPTG to induce expression. I hope that helps!

You can use pET 24 a+ plasmid and clone your gene of interest downstream of Ribosome Binding Site and T7 promotor sequence. But just the plasmid sequence is not enough. You also need to transform this plasmid into a strain which has T7 polymerase gene which is BL21DE3. The genomic DNA in this strain encodes T7 polymerase expression gene locked by lac promoter. Thus during induction, the IPTG (which mirrors lactose molecule but cannot be consumed by bacteria) molecule allows the expression of T& polyumerase which then attached itself to T7 promoter seqence to start transcribing the gene of interest downstream. Note there is also a leaky expression of this gene hence lac promotor is also kept between the T7 promotor and gene of interest.