OMP is located at 14 avenue E Belin in Toulouse, i.e. there on google map (look for the blue flag labelled IRAP site Belin).

The fastest way to get there from Toulouse-Blagnac airport is by taxi - which takes about 20 min and costs about 50 € one way. The best way to get there from downtown Toulouse is by public transport (called Tisseo in Toulouse, see next item) - which takes about 20 min and costs 1.5 € (single ticket). Using Tisseo from the airport to downtown is also possible, using either the Airport shuttle (about 30 min and 8 €) or the tram (same time, and cheaper) - both operated by Tisseo (see below). Altogether, using Tisseo from the airport to OMP takes about 1 hr including transfers.

Public transport in Toulouse is called Tisseo and involves a metro (2 main lines), trams (2 lines) and a network of buses. It also features the Airport Shuttle and a network of bike rentals called VeloToulouse (like Velib in Paris) with which you can pick a bike at one place and drop it somewhere else for the cost of one fare (i think).

You can use the static pdf map or the interactive map of all buses / metro / tram lines to plan your trips / connections. It allows you to work out itineraries between two different locations at specific dates / times, for instance between "Aéroport Blagnac" and "14 avenue Edouard Belin" (aka IRAP / OMP).

Fares are mentioned here - with an unlimited 3-day pass on metro / buses / trams costing for instance 10.5 € (as of 2015 Sept). Note that this pass does not include access to the Airport Shuttle but let you use tram T2 (that goes to the airport).