For example, this time 6 months ago I was 10 lbs lighter than I am now. But I'm a lot stronger now. I couldn't even do 135 lbs back squats (bar plus 45 lbs plate on each end) back then. Nowadays my routine consists of a few sets of back squats that culminates in a 10 repetition set of 315 lbs (bar plus 6x45 lbs plates). Physically, my weight is 10 lbs heavier now, but I have a lot less fat and so I'm a lot more compact in size.
I'm trying to lose some more fat, but when doing this there is always the real risk of losing muscle along with it. The scale does not tell the whole tale. By keeping tabs on how strong I am with respect to certain exercises, I can get a pretty good back-of-the-napkin kind of estimate of whether I'm losing fat or muscle.
When other people begin to notice changes depends heavily on your approach to "getting in shape". You can go fast and hard (and incorrectly). This might have you drop lots of weight the wrong way (e.g., losing lots of muscle a.k.a. the Oprah 1990s approach). A lot of commercial dieting programs depend on this strategy, because people will notice fairly soon (e.g., 1 month after starting). The early congratulatory praise by colleagues is encouraging and motivating to the dieter, causing them to keep going. If you go for a more gradual approach, people may not begin to notice for many months. That was the case for me this time around. People really didn't begin to notice until I bought some new clothes.
Because I lost weight so rapidly in high school, it was much more difficult for me to keep motivated this time around. Luckily, my friends whom I train with kept me focussed on metrics that could indicate progress such as how much weight I could push in an exercise and for how many repetitions. The goal this time around was to pack on muscle first, even if it meant gaining weight, and then to begin a cutting phase where I'd adopt an extremely strict diet and different exercise routine for a one or two month period.
Let me know if you're interested in some good resources. I didn't adopt any one plan. For example, I enjoyed the Hacker's Diet and while I think it's a good start, I personally felt like absolute shit most days when I treated a "calorie as a calorie". Whether I interpreted this incorrectly, the book says not to worry too much about what you eat so long as you pay attention to your caloric intake. Well, until I started eating nutritiously, I felt like crap, performed like crap at the gym, and while I did lose weight, I just didn't feel very healthy.
I'm not sure if you're personally interested, but if you're trying to get in shape I would allocate a 3 month window in which you think your chances of being stressed out are low and in which you can get lots of sleep and rest. You're going to be forcing your body to make so many changes that it'll really stress your immune system and ability to stay committed. In the first month, cut out stupid habits like excess drinking (or switch to vodka/soda from beer), eating half a pizza on a Friday night, downing tons of non-diet soda, etc.. This will be enough of a shock to your system, but you'll need to plough through 3 weeks of this to kill the bad habits.
In the next month, start increasing your physical activity while refraining from your previously bad eating habits. I'd tell you to get a personal trainer if you can afford one, but honestly the quality varies so much that it's risky. Perhaps you can seek out a friend who has a similar body type to your target, who can show you the ropes. Again, really push through the first 3 weeks until working out becomes as much of a priority as ensuring that you've done your backups or checked your code into the repository :-) Don't feel like you need to join a gym. The activity can be a sport, riding a bike to work, hiking, etc.. It just has to be consistent
In the third month, come back to your diet and begin to adopt healthier eating habits. Count your calories in everything that you eat to figure out where you're going overboard. Then make changes so that you come under your caloric requirements. I'd suggest 2000 calories as a good daily target intake for your average young male trying to lose weight this way. Any less and you probably won't get enough protein. Any more and you're probably eating too well. Increase your protein intake: if your target weight is 160 lbs then try to aim for 160 grams of protein a day (chicken breasts and eggs are your friends). If you're like most westerners, your meals are probably meat/poultry/fish supplemented with carbs and then rounded out with vegetables/fruits. Invert this last allocation so that your meals are supplemented with lots of vegetables/fruits and rounded out with a few carbs. In fact, if you really like vegetables, go to town on them. The more you eat the better you'll feel (it's a subjective thing) and they're generally so calorie-sparse as to be a non-worry.