push ups and chair pumps will do nothing more than tighten your muscles temporarily(well until you stop doing them on a regular basis).So you might end up looking more toned,again temporarily.
You say you have some weights,well thats a good start.no need for fancy equipment.
basically building muscle requires a good diet,and weight training.without a good diet,you will not gain muscle. the body has a maintenance level of calories.if you eat your maintenance amount of calories,you will neither gain nor lose weight.if you eat more than maintenance,you will gain weight(muscle or fat).if you eat less than maintenance calories,you will lose weight(muscle or fat).no two words about it.you cant fool the law of thermodynamics.
now what determines if your gains are fat or if they're muscle? its the partitioning of your macronutrients.For example,if you eat too many refined carbs,little protein,and high fat,your gains will be pure brown adipose tissue(fat) with little muscle.If you consume moderate complex carbs,moderate protein and low fat,you gains will be in the form of lean muscle mass with a tiny bit of fat,and this is what you want,lean mass.gaining fat is inevitable,theres no way to gain muscle and not gain an ounce of fat with it.you most likely will not notice the fat since it would be a 10:1 ratio of muscle vs. fat if you do it right.
you have to start counting calories if you want maximal results.if you just estimate,you might one day eat too many calories,and the next day you might eat less.this will sabotage your whole plan.you have to be consistent.either do it right,or dont do it at all.
if you give me your current weight,height,and waist size,i will give you a pretty accurate estimation of your maintenance calories.basically,what you want to do is eat 700 calories more than your maintenance level.
make sure you eat about 6-7 meals a day,split up evenly throughout your day.one of these meals will be a pre workout meal,which should consist of complex carbs(pasta,brown bread,legumes) and protein.have this meal 45 mins before you start working out.
another one of your meals is a post/after workout meal,which will be a sugary drink 15 mins after you finish working out. this can be gatorade,kool aid,powerade,tang. This will replenish your muscle glycogen stores and promote protein synthesis.Then after another 15 minutes,consume protein(doesnt have to be a protein shake,any protein source works).
Now this is what your workout routine should look like(for arms and chest).(you can rearange the excercises dates but keep them grouped the same)
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Monday: Biceps,forearms
Tuesday:triceps,chest
Wednesday:shoulders
Thursday:biceps,forearms
Friday:triceps,chest
Saturday:shoulders
Sunday:rest
I would advice you to workout your shoulders too,you don't want your body to look unproportional.Without shoulder training as well,you will look weird.
You want to do 2 excercises for each body part.3 sets of 10 reps each excercise.So for monday you'd do 2 excercises for biceps,3 sets of 10 reps each excercise.Then you would do 2 excercises for forearms.3 sets of 10 reps each excercise.Very simple.Don't even give yourself a time limit.You want quality lifts.
As for how much weight to use,well you have to find out through trial and error.Find an amount you can do comfortably(not too comfortable heh) for the amount of excercises, sets and reps.
thats basically it.follow the plan and watch your body go into a monster anabolic state.Theres no secrets or shortcuts to gaining muscle.Good diet + Good training routine = results,guaranteed.Training without good diet will do absolutely nothing positive.As a matter a fact,training when not on a good diet will cause you to lose muscle.After you train,your muscles are hungry to get replenished.If you dont feed them right,the body will break down your own muscle to make protein available for other muscles.You will accomplish nothing.On top of all that,you will slow down your metabolism tremendously and be highly suceptible to fat gains. take it from someone with experience. good luck
