How should I work out at the gym?

My boyfriend and I recently joined the local gym and we go Mon-Thurs. However I feel a bit lost when we go and it's all just as knew to my boyfriend as it is to me. This is my mon-Thurs work out rutine (sry I don't know the names of some of the equipment so i'll do my best to explain them.) I run on the eliptical for 5mins when we first get there. i then move on to this thing that is like a ginat foot peddel that you put your feet up against and push it with your feet. Then i do this thing where you put your feet on this bar and push your back into the seat and it's like doing crunches. I then run on the eliptical for another 5mins. After that i do this thing where you hold on to these two handles and plant your knee on a pad and push the bar with your other foot, than i switch feet. I then do this thing where you are pretty much doing the same thing but your on your stomach and you lift the bar with both legs. I then do this thing where you sit on it and you lift the bar with the top of your legs. After that I do this thing whereyou sit down and hold on to a bar with each hand and then push up. Then i do this thing where you sit with your chest into the pad and you hold on to two bard and swing your body from left to right. After all that i walk on the tredmill for 10mins. With all of the weights i do 30lbs except for the foot pedal thing , I do about 110lbs and I time each thing by songs. The avergae song is between 4-5 mins long so i figure i do each thing for about 10mins (give or take a few). Is this ok to do? I already know the basic such as eat right and drink plenty of water or sports drink while working out, I'm trying to lose at lease 60lbs.