It is important when you are looking for a training contract to network and attend as many events as possible where you will get exposed to different firms and current trainees and solicitors. This not only helps you meet new people and learn about firms (and potentially gets your name out there) but also helps improve your networking skills (or demonstrate that you can effectively network). If you are going to be a solicitor you will need to be able to network. You are not expected to be amazing at networking before you become a trainee – but every bit of practice helps!
When meeting contacts at different firms that you are genuinely interested in and you feel like you have made a reasonable connection or rapport with an individual – where possible and if appropriate, try and obtain their business card and follow up with a polite email to try and establish a contact. HOWEVER be cautious and sensitive to asking –you need to judge the situation right as not everyone will be willing to hand out business cards (the same applies to connecting on LinkedIn).
My personal rule is that I will hand my card to someone who I have built a rapport with and I feel like I can offer something to them (and/or they could have potential). If I refuse to give out my card it doesn’t automatically mean that I do not feel that person has what it takes it might simply be that I don’t feel like we talked enough or that I was not in a position where I could help them. But each time it is judged on a case by case basis.