My question is how should we go about it, once its up and running?
One thing I get in mind is to organize games between members.
Members playing each other is the main attraction for most successful clubs which you can do by organizing club competitions. The second attraction is playing games against non members which you can do by entering one or more teams in a local chess league.
My experience is that if you just have people coming and playing who they want they often get stuck in a rut playing the same 2 or 3 openings against the same 2 or 3 opponents every week. Organized club competitions get them playing a wider range of opponents.
Most clubs will have a club championship which runs over the season and which has a standard time control in which one game lasts most of the evening. This can either be a Swiss or, if you have a lot of members, a hybrid where you have group stages followed by a knockout between the winners of the groups.
Something which is a lot of fun is to organize blitz tournaments which take place with all games played in one evening. You don't necessarily want to do this every club evening but once or twice a month is a lot of fun and a 9 round blitz (if you have enough players) will get people playing a wider range of opponents.
A further twist to get players out of their ruts is to have themed blitz tournaments. This is where all the games played in the tournament must be the same opening. For example if the theme for the evening is the Ruy Lopez then all games start after the moves 1. e4 e5 2. Nf3 Nc6 3. Bb5 with black to move.
Apart from sets and clocks one other thing is very useful and that is a laptop with pairing software to help with organizing tournaments. Probably the best free program out there is the Vega pairing program. It is completely free to use on Linux and free on Windows for up to 30 players. Importantly it is simple and easy to use. It will also generate html for you to put details of your tournaments on your website if you have one.
There's also watching lectures, but who decides what lectures will we
Having lectures is a more tricky subject. You obviously want these to be given by the stronger players in the club. If you don't have any strong players then it is going to be difficult to get an interesting lecture. Ideally you get a small number of players to agree to take it in turns to give a lecture, say once a month, on an "interesting" topic. "Interesting" probably means not an opening since whatever opening you pick means it is automatically not interesting to all the players who don't play it and don't want to play it.
I'd suggest two types of topics, one for serious study and one for fun. The "serious study" one would be on endgames and endgame technique. The "fun study" one would be where a strong player analyzes one of their own games or perhaps an interesting game played by one of the club members, say the club championship final.
I don't know if there are any existing chess clubs in my city, though
it is unlikely.
Your best bet is to contact your national chess federation and ask them. They should be able to tell you if there are any other chess clubs in your area and give you contact details.